x^2+20x-264=0

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Solution for x^2+20x-264=0 equation: 


Simplifying
x2 + 20x + -264 = 0

Reorder the terms:
-264 + 20x + x2 = 0

Solving
-264 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '264' to each side of the equation.
-264 + 20x + 264 + x2 = 0 + 264

Reorder the terms:
-264 + 264 + 20x + x2 = 0 + 264

Combine like terms: -264 + 264 = 0
0 + 20x + x2 = 0 + 264
20x + x2 = 0 + 264

Combine like terms: 0 + 264 = 264
20x + x2 = 264

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 264 + 100

Reorder the terms:
100 + 20x + x2 = 264 + 100

Combine like terms: 264 + 100 = 364
100 + 20x + x2 = 364

Factor a perfect square on the left side:
(x + 10)(x + 10) = 364

Calculate the square root of the right side: 19.078784028

Break this problem into two subproblems by setting 
(x + 10) equal to 19.078784028 and -19.078784028.


Subproblem 1
x + 10 = 19.078784028

Simplifying
x + 10 = 19.078784028

Reorder the terms:
10 + x = 19.078784028

Solving
10 + x = 19.078784028

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 19.078784028 + -10

Combine like terms: 10 + -10 = 0
0 + x = 19.078784028 + -10
x = 19.078784028 + -10

Combine like terms: 19.078784028 + -10 = 9.078784028
x = 9.078784028

Simplifying
x = 9.078784028


Subproblem 2
x + 10 = -19.078784028

Simplifying
x + 10 = -19.078784028

Reorder the terms:
10 + x = -19.078784028

Solving
10 + x = -19.078784028

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -19.078784028 + -10

Combine like terms: 10 + -10 = 0
0 + x = -19.078784028 + -10
x = -19.078784028 + -10

Combine like terms: -19.078784028 + -10 = -29.078784028
x = -29.078784028

Simplifying
x = -29.078784028


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.078784028, -29.078784028}

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