x^2+32x+16=0

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Solution for x^2+32x+16=0 equation: 


Simplifying
x2 + 32x + 16 = 0

Reorder the terms:
16 + 32x + x2 = 0

Solving
16 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 32x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 32x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 32x + x2 = 0 + -16
32x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
32x + x2 = -16

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 = -16 + 256

Reorder the terms:
256 + 32x + x2 = -16 + 256

Combine like terms: -16 + 256 = 240
256 + 32x + x2 = 240

Factor a perfect square on the left side:
(x + 16)(x + 16) = 240

Calculate the square root of the right side: 15.491933385

Break this problem into two subproblems by setting 
(x + 16) equal to 15.491933385 and -15.491933385.


Subproblem 1
x + 16 = 15.491933385

Simplifying
x + 16 = 15.491933385

Reorder the terms:
16 + x = 15.491933385

Solving
16 + x = 15.491933385

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 = 15.491933385 + -16

Combine like terms: 16 + -16 = 0
0 + x = 15.491933385 + -16
x = 15.491933385 + -16

Combine like terms: 15.491933385 + -16 = -0.508066615
x = -0.508066615

Simplifying
x = -0.508066615


Subproblem 2
x + 16 = -15.491933385

Simplifying
x + 16 = -15.491933385

Reorder the terms:
16 + x = -15.491933385

Solving
16 + x = -15.491933385

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 = -15.491933385 + -16

Combine like terms: 16 + -16 = 0
0 + x = -15.491933385 + -16
x = -15.491933385 + -16

Combine like terms: -15.491933385 + -16 = -31.491933385
x = -31.491933385

Simplifying
x = -31.491933385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.508066615, -31.491933385}

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