x^2+36x+317=0

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Solution for x^2+36x+317=0 equation: 


Simplifying
x2 + 36x + 317 = 0

Reorder the terms:
317 + 36x + x2 = 0

Solving
317 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-317' to each side of the equation.
317 + 36x + -317 + x2 = 0 + -317

Reorder the terms:
317 + -317 + 36x + x2 = 0 + -317

Combine like terms: 317 + -317 = 0
0 + 36x + x2 = 0 + -317
36x + x2 = 0 + -317

Combine like terms: 0 + -317 = -317
36x + x2 = -317

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 = -317 + 324

Reorder the terms:
324 + 36x + x2 = -317 + 324

Combine like terms: -317 + 324 = 7
324 + 36x + x2 = 7

Factor a perfect square on the left side:
(x + 18)(x + 18) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 18) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 18 = 2.645751311

Simplifying
x + 18 = 2.645751311

Reorder the terms:
18 + x = 2.645751311

Solving
18 + x = 2.645751311

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 = 2.645751311 + -18

Combine like terms: 18 + -18 = 0
0 + x = 2.645751311 + -18
x = 2.645751311 + -18

Combine like terms: 2.645751311 + -18 = -15.354248689
x = -15.354248689

Simplifying
x = -15.354248689


Subproblem 2
x + 18 = -2.645751311

Simplifying
x + 18 = -2.645751311

Reorder the terms:
18 + x = -2.645751311

Solving
18 + x = -2.645751311

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 = -2.645751311 + -18

Combine like terms: 18 + -18 = 0
0 + x = -2.645751311 + -18
x = -2.645751311 + -18

Combine like terms: -2.645751311 + -18 = -20.645751311
x = -20.645751311

Simplifying
x = -20.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-15.354248689, -20.645751311}

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