x^2+33x-264=0

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Solution for x^2+33x-264=0 equation: 


Simplifying
x2 + 33x + -264 = 0

Reorder the terms:
-264 + 33x + x2 = 0

Solving
-264 + 33x + 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 + 33x + 264 + x2 = 0 + 264

Reorder the terms:
-264 + 264 + 33x + x2 = 0 + 264

Combine like terms: -264 + 264 = 0
0 + 33x + x2 = 0 + 264
33x + x2 = 0 + 264

Combine like terms: 0 + 264 = 264
33x + x2 = 264

The x term is 33x.  Take half its coefficient (16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
33x + 272.25 + x2 = 264 + 272.25

Reorder the terms:
272.25 + 33x + x2 = 264 + 272.25

Combine like terms: 264 + 272.25 = 536.25
272.25 + 33x + x2 = 536.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 536.25

Calculate the square root of the right side: 23.157072354

Break this problem into two subproblems by setting 
(x + 16.5) equal to 23.157072354 and -23.157072354.


Subproblem 1
x + 16.5 = 23.157072354

Simplifying
x + 16.5 = 23.157072354

Reorder the terms:
16.5 + x = 23.157072354

Solving
16.5 + x = 23.157072354

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = 23.157072354 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 23.157072354 + -16.5
x = 23.157072354 + -16.5

Combine like terms: 23.157072354 + -16.5 = 6.657072354
x = 6.657072354

Simplifying
x = 6.657072354


Subproblem 2
x + 16.5 = -23.157072354

Simplifying
x + 16.5 = -23.157072354

Reorder the terms:
16.5 + x = -23.157072354

Solving
16.5 + x = -23.157072354

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = -23.157072354 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -23.157072354 + -16.5
x = -23.157072354 + -16.5

Combine like terms: -23.157072354 + -16.5 = -39.657072354
x = -39.657072354

Simplifying
x = -39.657072354


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.657072354, -39.657072354}

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