2x^2+32x+118=0

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Solution for 2x^2+32x+118=0 equation: 


Simplifying
2x2 + 32x + 118 = 0

Reorder the terms:
118 + 32x + 2x2 = 0

Solving
118 + 32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(59 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(59 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
59 + 16x + x2 = 0

Solving
59 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-59' to each side of the equation.
59 + 16x + -59 + x2 = 0 + -59

Reorder the terms:
59 + -59 + 16x + x2 = 0 + -59

Combine like terms: 59 + -59 = 0
0 + 16x + x2 = 0 + -59
16x + x2 = 0 + -59

Combine like terms: 0 + -59 = -59
16x + x2 = -59

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -59 + 64

Reorder the terms:
64 + 16x + x2 = -59 + 64

Combine like terms: -59 + 64 = 5
64 + 16x + x2 = 5

Factor a perfect square on the left side:
(x + 8)(x + 8) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 8) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + 8 = 2.236067978

Simplifying
x + 8 = 2.236067978

Reorder the terms:
8 + x = 2.236067978

Solving
8 + x = 2.236067978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 2.236067978 + -8

Combine like terms: 8 + -8 = 0
0 + x = 2.236067978 + -8
x = 2.236067978 + -8

Combine like terms: 2.236067978 + -8 = -5.763932022
x = -5.763932022

Simplifying
x = -5.763932022


Subproblem 2
x + 8 = -2.236067978

Simplifying
x + 8 = -2.236067978

Reorder the terms:
8 + x = -2.236067978

Solving
8 + x = -2.236067978

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = -2.236067978 + -8

Combine like terms: 8 + -8 = 0
0 + x = -2.236067978 + -8
x = -2.236067978 + -8

Combine like terms: -2.236067978 + -8 = -10.236067978
x = -10.236067978

Simplifying
x = -10.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.763932022, -10.236067978}
Solution
x = {-5.763932022, -10.236067978}

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