# x^2+12x=33

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## Solution for x^2+12x=33 equation:

Simplifying
x2 + 12x = 33

Reorder the terms:
12x + x2 = 33

Solving
12x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 12x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 12x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + 12x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 12x + x2 = 0 + 33
12x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
12x + x2 = 33

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 33 + 36

Reorder the terms:
36 + 12x + x2 = 33 + 36

Combine like terms: 33 + 36 = 69
36 + 12x + x2 = 69

Factor a perfect square on the left side:
(x + 6)(x + 6) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting
(x + 6) equal to 8.306623863 and -8.306623863.

Subproblem 1x + 6 = 8.306623863

Simplifying
x + 6 = 8.306623863

Reorder the terms:
6 + x = 8.306623863

Solving
6 + x = 8.306623863

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 8.306623863 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8.306623863 + -6
x = 8.306623863 + -6

Combine like terms: 8.306623863 + -6 = 2.306623863
x = 2.306623863

Simplifying
x = 2.306623863

Subproblem 2x + 6 = -8.306623863

Simplifying
x + 6 = -8.306623863

Reorder the terms:
6 + x = -8.306623863

Solving
6 + x = -8.306623863

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -8.306623863 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8.306623863 + -6
x = -8.306623863 + -6

Combine like terms: -8.306623863 + -6 = -14.306623863
x = -14.306623863

Simplifying
x = -14.306623863

SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {2.306623863, -14.306623863}`