x^2+22x-117=0

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Solution for x^2+22x-117=0 equation: 


Simplifying
x2 + 22x + -117 = 0

Reorder the terms:
-117 + 22x + x2 = 0

Solving
-117 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '117' to each side of the equation.
-117 + 22x + 117 + x2 = 0 + 117

Reorder the terms:
-117 + 117 + 22x + x2 = 0 + 117

Combine like terms: -117 + 117 = 0
0 + 22x + x2 = 0 + 117
22x + x2 = 0 + 117

Combine like terms: 0 + 117 = 117
22x + x2 = 117

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 117 + 121

Reorder the terms:
121 + 22x + x2 = 117 + 121

Combine like terms: 117 + 121 = 238
121 + 22x + x2 = 238

Factor a perfect square on the left side:
(x + 11)(x + 11) = 238

Calculate the square root of the right side: 15.427248621

Break this problem into two subproblems by setting 
(x + 11) equal to 15.427248621 and -15.427248621.


Subproblem 1
x + 11 = 15.427248621

Simplifying
x + 11 = 15.427248621

Reorder the terms:
11 + x = 15.427248621

Solving
11 + x = 15.427248621

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 15.427248621 + -11

Combine like terms: 11 + -11 = 0
0 + x = 15.427248621 + -11
x = 15.427248621 + -11

Combine like terms: 15.427248621 + -11 = 4.427248621
x = 4.427248621

Simplifying
x = 4.427248621


Subproblem 2
x + 11 = -15.427248621

Simplifying
x + 11 = -15.427248621

Reorder the terms:
11 + x = -15.427248621

Solving
11 + x = -15.427248621

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -15.427248621 + -11

Combine like terms: 11 + -11 = 0
0 + x = -15.427248621 + -11
x = -15.427248621 + -11

Combine like terms: -15.427248621 + -11 = -26.427248621
x = -26.427248621

Simplifying
x = -26.427248621


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.427248621, -26.427248621}

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