SOLUTION: Please help me solve this equation; use the method of completing the square, solve 5x^2+32x+10=0.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve this equation; use the method of completing the square, solve 5x^2+32x+10=0.      Log On


   

Question 1123995: Please help me solve this equation; use the method of completing the square, solve 5x^2+32x+10=0.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
equation is 5x^2 + 32x + 10 = 0

subtract 10 from both sides of the equation to get:

5x^2 + 32x = -10

divide both sides of the equation by 5 to get:

x^2 + 32/5 * x = -10 / 5

simplify to get:

x^2 + 6.4x = -2

take half the coefficient of the x term to get:

(x + 3.2)^2 - 3.2^2 = -2

add 3.2^2 to both sides of the equation to get:

(x + 3.2)^2 = -2 + 3.2^2

simplify to get:

(x + 3.2)^2 = -2 + 10.24

simplify further to get:

(x + 3.2)^2 = 8.24

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

x + 3.2 = 2.870540019

subtract 3.2 from both sides of the equation to get:

x = -.3294599811

confirm by replaceing x in the original equation to see that it's true.

5x^2 + 32x + 10 = 0 becomes 5 * -.3294599811 + 32 * -.3294599811 + 10 = 0 which becomes 0 - 0, confirming the solution is good.

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

that was the purpose for dividing both sides of the equation by 5.

the part that completes the square is when you take the x^2 + bx part of the euaion and then take half the b term to form the squaring factors.

x^2 + bx becomes (x + b/2)^2 - (b/2)^2.

the - (b/2)^2 part then gets added to both sides of the equation.

some instructions skip the minus part and just add it directly.

they'll say:

x^2 + bx = c becomes (x + b/2)^2 = c + (b/2)^2.

they'll skip the part that it was first (x + b/2)^2 - (b/2)^2 = c and then adding (b/2)^2 to both sides of the equation.

here's a reference on completing the square you might find useful.

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

why there is the subtraction is captured below:

take x^2 + 20x

you want to make it (x + 10)^2 = x^2 + 20x

but (x + 10)^2 = x^2 + 20x + 10^2

so, in order to make (x + 10)^2 = x^2 + 20x, you have to subtract 10^2 from it.

you get (x + 10)^2 - 10^2 = x^2 + 20x + 10^2 - 10^2 which makes it (x + 10)^2 - 10^2 = x^2 + 20x.




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation; use the method of completing the square, solve 5x^2+32x+10=0.
matrix%281%2C3%2C+5x%5E2+%2B+32x+%2B+10%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+5%28x%5E2+%2B+%2832%2F5%29x+%2B+10%2F5%29%2C+%22=%22%2C+5%280%29%29 --- Dividing by 5 to make the coefficient on the x2, 1

matrix%281%2C3%2C+x%5E2+%2B+%2832%2F5%29x+%2B+2%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+x%5E2+%2B+%2832%2F5%29x%2C+%22=%22%2C+-+2%29 ------------ Subtracting 2 to move constant to right of equals sign

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

matrix%281%2C3%2C+%28x+%2B+16%2F5%29%5E2%2C+%22=%22%2C+-+2+%2B+256%2F25%29

matrix%281%2C3%2C+%28x+%2B+16%2F5%29%5E2%2C+%22=%22%2C+-+50%2F25+%2B+256%2F25%29

matrix%281%2C3%2C+%28x+%2B+16%2F5%29%5E2%2C+%22=%22%2C+206%2F25%29

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

matrix%281%2C3%2C+x+%2B+16%2F5%2C+%22=%22%2C+%22+%22%2B-+sqrt%28206%29%2F5%29

matrix%281%2C3%2C+x%2C+%22=%22%2C+%22+%22+%2B-+sqrt%28206%29%2F5+-+16%2F5%29

 

You can convert these to decimal forms if you so choose!