x^2+32x+100=0

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Solution for x^2+32x+100=0 equation: 


Simplifying
x2 + 32x + 100 = 0

Reorder the terms:
100 + 32x + x2 = 0

Solving
100 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 32x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + 32x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 32x + x2 = 0 + -100
32x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
32x + x2 = -100

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 = -100 + 256

Reorder the terms:
256 + 32x + x2 = -100 + 256

Combine like terms: -100 + 256 = 156
256 + 32x + x2 = 156

Factor a perfect square on the left side:
(x + 16)(x + 16) = 156

Calculate the square root of the right side: 12.489995997

Break this problem into two subproblems by setting 
(x + 16) equal to 12.489995997 and -12.489995997.


Subproblem 1
x + 16 = 12.489995997

Simplifying
x + 16 = 12.489995997

Reorder the terms:
16 + x = 12.489995997

Solving
16 + x = 12.489995997

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 = 12.489995997 + -16

Combine like terms: 16 + -16 = 0
0 + x = 12.489995997 + -16
x = 12.489995997 + -16

Combine like terms: 12.489995997 + -16 = -3.510004003
x = -3.510004003

Simplifying
x = -3.510004003


Subproblem 2
x + 16 = -12.489995997

Simplifying
x + 16 = -12.489995997

Reorder the terms:
16 + x = -12.489995997

Solving
16 + x = -12.489995997

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 = -12.489995997 + -16

Combine like terms: 16 + -16 = 0
0 + x = -12.489995997 + -16
x = -12.489995997 + -16

Combine like terms: -12.489995997 + -16 = -28.489995997
x = -28.489995997

Simplifying
x = -28.489995997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.510004003, -28.489995997}

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