x^2+32x+80=0

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Solution for x^2+32x+80=0 equation: 


Simplifying
x2 + 32x + 80 = 0

Reorder the terms:
80 + 32x + x2 = 0

Solving
80 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + 32x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + 32x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + 32x + x2 = 0 + -80
32x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
32x + x2 = -80

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = -80 + 256

Reorder the terms:
256 + 32x + x2 = -80 + 256

Combine like terms: -80 + 256 = 176
256 + 32x + x2 = 176

Factor a perfect square on the left side:
(x + 16)(x + 16) = 176

Calculate the square root of the right side: 13.266499161

Break this problem into two subproblems by setting 
(x + 16) equal to 13.266499161 and -13.266499161.


Subproblem 1
x + 16 = 13.266499161

Simplifying
x + 16 = 13.266499161

Reorder the terms:
16 + x = 13.266499161

Solving
16 + x = 13.266499161

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 13.266499161 + -16

Combine like terms: 16 + -16 = 0
0 + x = 13.266499161 + -16
x = 13.266499161 + -16

Combine like terms: 13.266499161 + -16 = -2.733500839
x = -2.733500839

Simplifying
x = -2.733500839


Subproblem 2
x + 16 = -13.266499161

Simplifying
x + 16 = -13.266499161

Reorder the terms:
16 + x = -13.266499161

Solving
16 + x = -13.266499161

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -13.266499161 + -16

Combine like terms: 16 + -16 = 0
0 + x = -13.266499161 + -16
x = -13.266499161 + -16

Combine like terms: -13.266499161 + -16 = -29.266499161
x = -29.266499161

Simplifying
x = -29.266499161


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.733500839, -29.266499161}

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