Solve 2x^2 + x - 15 = 0

Answers

Answer 1

Step-by-step explanation:

[tex] \tt{2 {x}^{2} + x - 15 = 0}[/tex]

USING THE QUADRATIC FORMULA :

Here ,

a = 2 , b = 1 and c = - 15

Substitute the values into the quadratic equation :

⇾ [tex] \tt{x \: = \: \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} \: }{2a} }[/tex]

⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {1}^{2} - 4 \times 2 \times ( - 15) } }{2 \times 2}} [/tex]

Simplify

⇾ [tex] \tt{x = \frac{ -1 \:± \sqrt{1 - 8 \times ( - 15)} }{4}} [/tex]

⇾ [tex] \tt{x = \frac{ - 1\:± \: \sqrt{1 + 120} }{4}} [/tex]

⇾ [tex] \tt{x = \frac{ - 1 \:± \: \sqrt{121} }{4}} [/tex]

⇾ [tex] \tt{x = \frac{ - 1\: ± \: \sqrt{ {11}^{2} } }{4}} [/tex]

⇾ [tex] \tt{x = \frac{ - 1 \:± \: 11 }{4}} [/tex]

Now , we can split this into two answers because of the plus minus ( ± ) symbol.

Taking positive ( + ) sign :

⇾ [tex] \tt{x = \frac{ - 1+ 11}{4}} [/tex]

⇾ [tex] \tt{x = \frac{10}{4}} [/tex]

⇾ [tex] \boxed{ \tt{x = \frac{5}{2} }}[/tex]

Again , taking negative ( - ) sign :

⇾ [tex] \tt{x = \frac{ - 1 - 11}{4}} [/tex]

⇾ [tex] \tt{x = \frac{ - 12}{4}} [/tex]

⇾[tex] \boxed{ \tt{x = - 3}}[/tex]

☥ [tex] \red{ \bold{ \boxed{ \boxed{ \tt{Our \: final \: answer : x = \frac{5}{2} \: or \: - 3}}}}}[/tex]

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[tex] \underline{ \underline{ \sf{Explore \: more !!}}} : [/tex]

There are various methods of solving quadratic equations. They are as follows :

Solving a quadratic equation by factorisation method : In this method , the second order of polynomial ax² + bx + c is factorised and expressed as the product of two linear factors. Then each linear factors is separately solved to get the required solutions of the equation by applying zero factor property. In zero factor property , if p • q = 0 then either p = 0 or q = 0 .In other words , if the product of two numbers is 0 , then one or both of the numbers must be zero.

Solving a quadratic equation by completing the square : In this method , we transpose the constant term ( c ) to R.H.S , then L.H.S to expressed as perfect square expression.

Solving a quadratic equation by using formula : In solving a quadratic equation of the form ax² + bx + c = 0 by completing the square , we obtain two roots of x , which are :[tex] \sf{ \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex] and [tex] \sf{ \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a}} [/tex]. These roots can be written as [tex] \sf{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a}} [/tex] where a is the coefficient of x² , b is the coefficient of x and c is the constant term. We use this formula to find the required solutions of the given quadratic equation.

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Answer 2

The solutions to the quadratic equation [tex]2x^{2} + x - 15[/tex]  are x = 2.5 and x = -3.

Given data:

The quadratic equation is represented as  [tex]2x^{2} + x - 15[/tex].

Now, the roots are determined as:

[tex]x_{1}=\frac{-b+\sqrt[]{b^{2}-4ac} }{2a}[/tex]

[tex]x_{2}=\frac{-b-\sqrt[]{b^{2}-4ac} }{2a}[/tex]

The value of a = 2 , b = 1, and c = -1.5

Substituting the values in the equation:

[tex]x_{1}=\frac{-1+\sqrt[]{1^{2}-4*2*(-1.5)} }{2*2}[/tex]

So, the value of [tex]x_{1}=2.5[/tex].

[tex]x_{2}=\frac{-1-\sqrt[]{1^{2}-4*2*(-1.5)} }{2*2}[/tex]

The value of [tex]x_{2}=-3[/tex].

So, the roots are x = 2.5 and x = -3.

Hence, the quadratic equation is solved.

To learn more about quadratic equations, refer:

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Related Questions

PLZ I NEED ANSWERS. THIS IS MIDDLE SCHOOL LEVEL NOT COLLEGE
Select ALL the expressions that are greater than one

A: 4 Divided by 3/4
B: 1/3 Divided by 10
C: 5/6 Divided by 2/5
D: 3 1/8 Divided by 2 7/8
E: 9/7 divided by 8/7

Answers

All are greater than 1 except for letter B.

Answer: The answers are all of the options except for B.

Step-by-step explanation:

Option A. 4/1 x 4/3 is 16/3. 16/3 > 1

Option B. 1/3 x 1/10 is 1/30. 1/30 < 1

Option C. 5/6 x 5/2 is 25/12. 25/12 > 1

Option D. 25/8 x 8/23 is 200/184. 200/184 > 1

Option E. 9/7 x 7/8 is 63/56. 63/56 > 1

Hence, the correct answer is option A, C, D, and E.

I need the simplified expression for this please ​

Answers

Answer:

16x+5

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf 16x+5}[/tex]

Step-by-step explanation:

[tex]\sf 5(2x-1)+2(3x+5)\\\\Expanding \ Parenthesis\\\\= 10 x -5+6x+10\\\\Combining \ like \ terms\\\\= 10x+6x-5+10\\\\=16x + 5\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the following loans meet Melanie’s criteria?

Loan A: 9.265% nominal rate, compounded weekly
Loan B: 9.442% nominal rate, compounded monthly
Loan C: 9.719% nominal rate, compounded quarterly
a.
B only
b.
A and C
c.
A and B
d.
None of these fit Melanie’s criteria.

Answers

Answer:

The correct answer is C.

Step-by-step explanation:

Giving the following information:

Loan A: 9.265% nominal rate, compounded weekly

Loan B: 9.442% nominal rate, compounded monthly

Loan C: 9.719% nominal rate, compounded quarterly

To calculate the effective annual rate, we need to use the following formula:

Effective annual rate= [(1+i)^n] - 1

Loan A:

i= 0.09265/52= 0.001782

Effective annual rate= [(1.001782^52) - 1]

Effective annual rate= 0.097 = 9.7%

Loan B:

i= 0.09442/12= 0.007868

Effective annual rate= [(1.007868^12) - 1]

Effective annual rate= 0.0986 = 9.86%

Loan C:

i= 0.09719/4= 0.02439

Effective annual rate= [(1.02439^4) - 1]

Effective annual rate= 10.11%

Answer:

c

Step-by-step explanation:

A computer is normally $550 but is discounted to $385. What percent of the original price does Mark pay?

Can someone help me?

Answers

Answer:

70%

Step-by-step explanation:

385/550 giving you a decimal of 0.7 which is 70%


Write an equation for the n
term of
the arithmetic sequence:
15, 28, 41, ...​

Answers

Answer:

13n+2

Step-by-step explanation:

find the difference between the numbers which is 13

》13n

from 13 to 15 you add 2

》13n+2

The graph of a system of linear equations with the same slope and the same y-intercepts will have no solutions.
Always
Sometimes
Never

Answers

Answer:

Never

Step-by-step explanation:

If two equations have the same slopes and the same y-intercepts they are equivalent to each other

Here's why:

The formula for a linear equation is y= mx +b

b= y- intercept

m= slope

m and b are only variable that have to be replaced by a number for the equation to be complete

Therefore, when m and b (or the slope and the y-intercept)  of both equations are the same, the two equations are the same

The answer would be allrealnumbers, not nosolutions

Hope this helps!!!

Carol had a previous balance of $557.83 in her checking account. She deposited checks
totaling $882.84, made cash withdrawals of $325.00, and wrote checks totaling
$617.77 that were paid by the bank. She also earned interest of $1.15. What is her
present balance?
(Present Balance = Previous Balance + Deposits - Withdrawals - Service Charges/Fees
+ Interest)
c) $496.75
b) $499.05
a) $2.384.59
d) $1.149.05

Answers

Answer:

x^2-4/7x-12/49=0

x= 6/7 and -2/7

Step-by-step explanation:

Round to the nearest whole number: 123.45

Answers

Answer:

123

Step-by-step explanation:

because if its lower than 50 you round down, if its 50 or above you round up

Answer:  

If you like to round 123.45 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post. Number:.

Step-by-step explanation:

How many times greater is the value of the 4 In 42,672 than the value of the 4 in 37,426

Answers

Step-by-step explanation:

it 100 more than the 4 in 37,426

What is the x-intercept of the following equation? 4x + 2y = 12

Answers

Answer:

3

Step-by-step explanation:

8936245x18463 brainlist to who gets this right

Answers

164989891435 I think lol

Oceanside Bike Rental Shop charges a 15 dollar fixed fee plus 9 dollars an hour for renting a bike. Dan paid 69 dollars to rent a bike. Which equation when solved would show how many hours the bike was rentented? Let h = hours

Answers

Answer:

Step-by-step explanation:

Dan paid  69 divided by 9 = H - 15

Given that XH bisects Answer choices
A.) 50
B.) 48
C.) 62
D.) none of the above

Answers

We know CXD form a 90 degree angle, plus 32 that is angle BXC
90+32=122
We also know XH bisects this angle, which means it cut it in half,
122/2= 61

Answer: 61

what is different of the four shapes?​

Answers

Answer:

It has only 1 pair of parallel sides.

Step-by-step explanation:

Answer:

It has only 1 pair of parallel sides

Step-by-step explanation:

The coordinates of the vertices of △XYZ are X(−5, 5), Y(−3, −2), and Z(4, 0). The slope of XZ is __, the slope of YZ is __, and the slope of XY is __. △XYZ __ a right triangle because ____________.

-7/2 -5/9 -2/7 2/7 9/5 is is not no two of these slopes have a product of -1 two of these problems have a product of -1

Answers

Answer:

Slope of XZ = -5/9

Slope of YZ  = 2/7

Slope of XY  = -7/2

Step-by-step explanation:

Slope is expressed as;

m = y2-y1/x2-x1

For XZ

X(−5, 5), and Z(4, 0)

Slope of XZ = 0-5/4-(-5)

Slope of XZ = -5/4+5

Slope of XZ = -5/9

For YZ

Y(−3, −2), and Z(4, 0).

Slope of YZ = 0-(-2)/4-(-3)

Slope of YZ = 2/4+3

Slope of YZ  = 2/7

For XY

X(−5, 5), Y(−3, −2)

Slope of XY = -2-5/-3-(-5)

Slope of XY = -7/-3+5

Slope of XY = -7/2

For two lines to be perpendicular, the product of their slope must be -1

Taking the product of XY and YZ

mXY * mYZ = -7/2 * 2/7

mXY * mYZ  = -1

since the product of mXY and mYZ is -1. this shows that line XY is perpendicular to YZ and showing that the triangle XYZ is right triangle

Compote table please help me please?

Answers

2
5
8
9
10
that what I got

1. A family eats at a restaurant. The bill is $42. They have a coupon that gives them 15% off
their meal. The family then leaves a 20% tip.
a. How much did the family spend on the meal after the coupon?
b. How much did the family spend on the meal in total?

Answers

a.Solution:

[tex]42 - 42 \times 15\%[/tex]

[tex] =42 - 42 \times \frac{15}{100} [/tex]

[tex] =42 - 21 \times \frac{15}{50} [/tex]

[tex] =42 - \frac{315}{50} [/tex]

[tex] = 42 - 6 \: \frac{15}{50} [/tex]

[tex] = 41 \: \frac{50}{50} - 6 \: \frac{15}{50} [/tex]

[tex] = 35 \: \frac{35}{50} [/tex]

[tex] = 35.70[/tex]

Answer:

The family did spend $35.70 on the meal after the coupon

b.Solution:

[tex]35.70 + 42 \times 20\%[/tex]

[tex] = 35.70 + 42 \times 0.2[/tex]

[tex] = 35.70 + 8.4[/tex]

[tex] = 44.10[/tex]

Answer:

The family did spend $44.10 on the meal in total.

#CarryOnLearning

#AnswerForTrees

#BrainlyBookSmart

which expression is equivalent to 3(7v)

Answers

From what I remember it is 21 v

A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall. Which of the following absolute values best represents this restriction, where h represents height?

Answers

Answer:

|h-57.5| less than or equal to 7.5

Step-by-step explanation:

Since the question states that a child must be 50 and 65 inches, plug in values that are within this range and determine which answer choice gives a TRUE relationship. Choose 60 for h.

Also, I just did it.

Are the two triangles above similar? Why or why not?
A. Yes, they are similar by the AA similarity postulate.
B. Yes, they are similar by the SAS similarity theorem.
C. No, two congruent angles is not enough information to prove similarity.
D. No, triangles with two congruent angles are never similar.

Answers

Answer:

is it c??

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because of the dashes on the angles, angle A is congruent to angle D and angle B is congruent to angle E. Since we know that 2 angles are congruent, the triangles are similar because of AA similarity

Simplify: [-5]+2 answer please ​

Answers

Answer:

I think it's -3

hope it's right:)

Step-by-step explanation:

[tex] \sf{ \huge{( - 5) + 2}}[/tex]

While adding or subtracting integers with unlike signs , subtract and keep the sign of the higher integer. In our case , subtract 2 from 5 and keep the sign of higher integer i.e ( - )

⟿ [tex] \sf{ \huge{ \boxed{ { - 3}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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What is the domain of f(x) = 5^x - 7?

A.) {x| x > -7}
B.) {x| x < -7}
C.) {x| x > 0}
D.) {x| x is a real number}

Answers

Answer:

D

Step-by-step explanation:

I think the intervals can pretty much be infinite.

First person to answer will get 100 points & Brainliest!

Answers

Answer:

heyyyyyy

Step-by-step explanation:

i am thinking of a number x. What algebraic expression represents "eight less than three times this number "?​

Answers

Answer:

3x-8

Step-by-step explanation:

3x is three times the number, -8 is 8 less.

Potato salad can be purchased at the grocery store for $2.58 per pound. If Michael wants to buy 2.5 pounds of potato salad, how much will it cost?​

Answers

Answer: $6.45

Step-by-step explanation: Since 1 pound is $2.58, and we need to find out how much is 2.5 pounds, we can just multiply 2.58 by 2.5. Should be simple for you. Hope this helps. :)

$6.95 is what it wold cost to purchase 2.5lb of potato salad

Max delivers 8,520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in 2 months? Solve the problem and explain the steps you took to solve.​

Answers

Answer:

Because there are 12 months in a year the ratio of the number of pieces of mail Max delivers in 12 months can be written as: 852012 or 7101 (720 pieces of mail per month).

Answer:

He would deliver 1420 mails in 2 month's

Step-by-step explanation:

First, I divided 8,520 by 12 because 12 month's in one 1 year

Then, I get 710, that is the amount he delivers each month

Lastly, I multiply 710 by 2 because that is the amount for 2 month's and it equals 1,420 so, the answer is 1,420 :)

Explain how you can use multiplication to solve a division problem.​

Answers

Answer:Inverse operation

Step-by-step explanation: an example is 5 x 5. That equals 25 so take 5 and divide that by 5. Inverse operation is important.  

The rectangle shown has a perimeter of 84 cm and the given area. Its length is 6 more than 5 times its width. Write and solve a system of equations to find the dimensions of the rectangle.

Answers

The answer is that the Width is equal to 10 and the length is equal to 36

Help me please! I don’t understand! I’ll give you brainly!

Answers

Answer:

For number 2 it is = x(f + h)

For number 3 it is = x(g + h)

For number 4 it is = x(h + f)

For number 5 it is = x(f - g)

Hope this helps:)

Probability Questions Help is needed plzzzzzzzzzz

Answers

Answer: 0.0049 hope this is right

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