x^2+22x-180=0

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Solution for x^2+22x-180=0 equation: 


Simplifying
x2 + 22x + -180 = 0

Reorder the terms:
-180 + 22x + x2 = 0

Solving
-180 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 22x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 22x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 22x + x2 = 0 + 180
22x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
22x + x2 = 180

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 = 180 + 121

Reorder the terms:
121 + 22x + x2 = 180 + 121

Combine like terms: 180 + 121 = 301
121 + 22x + x2 = 301

Factor a perfect square on the left side:
(x + 11)(x + 11) = 301

Calculate the square root of the right side: 17.349351573

Break this problem into two subproblems by setting 
(x + 11) equal to 17.349351573 and -17.349351573.


Subproblem 1
x + 11 = 17.349351573

Simplifying
x + 11 = 17.349351573

Reorder the terms:
11 + x = 17.349351573

Solving
11 + x = 17.349351573

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 = 17.349351573 + -11

Combine like terms: 11 + -11 = 0
0 + x = 17.349351573 + -11
x = 17.349351573 + -11

Combine like terms: 17.349351573 + -11 = 6.349351573
x = 6.349351573

Simplifying
x = 6.349351573


Subproblem 2
x + 11 = -17.349351573

Simplifying
x + 11 = -17.349351573

Reorder the terms:
11 + x = -17.349351573

Solving
11 + x = -17.349351573

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 = -17.349351573 + -11

Combine like terms: 11 + -11 = 0
0 + x = -17.349351573 + -11
x = -17.349351573 + -11

Combine like terms: -17.349351573 + -11 = -28.349351573
x = -28.349351573

Simplifying
x = -28.349351573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.349351573, -28.349351573}

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