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 1

x + 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 2

x + 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

Solution

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

 

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