SOLUTION: Please help me solve this equation by method of completing the square method: 2x^2+13x-15=0

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Question 1123897: Please help me solve this equation by method of completing the square method: 2x^2+13x-15=0
Found 3 solutions by Theo, MathTherapy, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:

2x^2 + 13x = 15

divide both sides of this equation by 2 to get:

x^2 + 6.5x = 7.5

take half the coefficient of the x term to get:

(x + 3.25)^2 - 3.25^2 = 7.5

simplify to get:

(x + 3.25)^2 - 10.5625 = 7.5

add 10.5625 to both sides of the equation to get:

(x + 3.25)^2 = 7.5 + 10.5625

simplify to get:

(x + 3.25)^2 = 18.0625

take the square root of both sides of this equation to get:

x + 3.25 = 4.25

subtract 3.25 from both sides of this equation to get:

x = 1

that's your solution.

confirm by replacing x with 1 in the original equation.

2x^2 + 13x = 15 becomes 2*1^2 + 13*1 = 15

simplify to get 2 + 13 = 15

combine like terms to get 15 = 15

this confirms the solution is correct.

here's a reference on completing the squares method of solving quadratic equations.

https://www.purplemath.com/modules/sqrquad.htm

when completing the square, the coefficient of the x^2 term needs to be 1.

that's why i divided both sides of the equation by 2 when i started.

the equation then became x^2 + 6.5x = 7.5

i then took half the coefficient of the x term to get:

(x + 3.25)^2 - 3.25^2 = 7.5

the reason for this is as follows:

(x + 3.25)^2 = x^2 + 6.5x + 3.25^2

since i wanted (x + 3.5)^2 to be equal to x^2 + 6.5x, i needed to subtract 3.25^2 from the result.

that resulted in (x + 3.25)^2 = x^2 + 6.5x + 3.25^2 -3.25^2 = x^2 + 6.5x

in other words, x^2 + 6.5x is equal to (x + 3.25)^2 - 3.25^2

so i wound up with x^2 + 6.5x = 7.5 becoming (x + 3.25)^2 - 3.25^2 = 7.5

the rest was solving for x as i did above.







Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation by method of completing the square method: 2x^2+13x-15=0
matrix%281%2C3%2C+2x%5E2+%2B+13x+-+15%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+2%28x%5E2+%2B+%2813%2F2%29x+-+15%2F2%29%2C+%22=%22%2C+2%280%29%29 --- Dividing by 2 to make the coefficient on the x2, 1

matrix%281%2C3%2C+x%5E2+%2B+%2813%2F2%29x+-+15%2F2%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+x%5E2+%2B+%2813%2F2%29x%2C+%22=%22%2C+15%2F2%29 ------------- Adding 15%2F2 to move constant to right of equals sign

 ------ Taking 1%2F2 of b, squaring it, and then ADDING the result to both sides of equation

matrix%281%2C3%2C+%28x+%2B+13%2F4%29%5E2%2C+%22=%22%2C+120%2F16+%2B+169%2F16%29

matrix%281%2C3%2C+%28x+%2B+13%2F4%29%5E2%2C+%22=%22%2C+289%2F16%29

 ------- Taking square root of both sides

matrix%281%2C3%2C+x+%2B+%2813%2F4%29%2C+%22=%22%2C+%22+%22%2B-+17%2F4%29

matrix%281%2C3%2C+x%2C+%22=%22%2C+%22+%22+%2B-+17%2F4+-+13%2F4%29

 ========> 

ANY other answer is INCORRECT, so SIMPLY IGNORE!

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
On completing the square method see the lesson
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.