x^2+36x+176=0

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Solution for x^2+36x+176=0 equation: 


Simplifying
x2 + 36x + 176 = 0

Reorder the terms:
176 + 36x + x2 = 0

Solving
176 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-176' to each side of the equation.
176 + 36x + -176 + x2 = 0 + -176

Reorder the terms:
176 + -176 + 36x + x2 = 0 + -176

Combine like terms: 176 + -176 = 0
0 + 36x + x2 = 0 + -176
36x + x2 = 0 + -176

Combine like terms: 0 + -176 = -176
36x + x2 = -176

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -176 + 324

Reorder the terms:
324 + 36x + x2 = -176 + 324

Combine like terms: -176 + 324 = 148
324 + 36x + x2 = 148

Factor a perfect square on the left side:
(x + 18)(x + 18) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + 18) equal to 12.165525061 and -12.165525061.


Subproblem 1
x + 18 = 12.165525061

Simplifying
x + 18 = 12.165525061

Reorder the terms:
18 + x = 12.165525061

Solving
18 + x = 12.165525061

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 12.165525061 + -18

Combine like terms: 18 + -18 = 0
0 + x = 12.165525061 + -18
x = 12.165525061 + -18

Combine like terms: 12.165525061 + -18 = -5.834474939
x = -5.834474939

Simplifying
x = -5.834474939


Subproblem 2
x + 18 = -12.165525061

Simplifying
x + 18 = -12.165525061

Reorder the terms:
18 + x = -12.165525061

Solving
18 + x = -12.165525061

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -12.165525061 + -18

Combine like terms: 18 + -18 = 0
0 + x = -12.165525061 + -18
x = -12.165525061 + -18

Combine like terms: -12.165525061 + -18 = -30.165525061
x = -30.165525061

Simplifying
x = -30.165525061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.834474939, -30.165525061}

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