x^2+2x^2=36x+72

Solution for x^2+2x^2=36x+72 equation:

Simplifying
x2 + 2x2 = 36x + 72

Combine like terms: x2 + 2x2 = 3x2
3x2 = 36x + 72

Reorder the terms:
3x2 = 72 + 36x

Solving
3x2 = 72 + 36x

Solving for variable 'x'.

Reorder the terms:
-72 + -36x + 3x2 = 72 + 36x + -72 + -36x

Reorder the terms:
-72 + -36x + 3x2 = 72 + -72 + 36x + -36x

Combine like terms: 72 + -72 = 0
-72 + -36x + 3x2 = 0 + 36x + -36x
-72 + -36x + 3x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-72 + -36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -12x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-24 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + -12x + x2 = 0

Solving
-24 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -12x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -12x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -12x + x2 = 0 + 24
-12x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-12x + x2 = 24

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 = 24 + 36

Reorder the terms:
36 + -12x + x2 = 24 + 36

Combine like terms: 24 + 36 = 60
36 + -12x + x2 = 60

Factor a perfect square on the left side:
(x + -6)(x + -6) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + -6) equal to 7.745966692 and -7.745966692.

Subproblem 1
x + -6 = 7.745966692

Simplifying
x + -6 = 7.745966692

Reorder the terms:
-6 + x = 7.745966692

Solving
-6 + x = 7.745966692

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 = 7.745966692 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.745966692 + 6
x = 7.745966692 + 6

Combine like terms: 7.745966692 + 6 = 13.745966692
x = 13.745966692

Simplifying
x = 13.745966692

Subproblem 2
x + -6 = -7.745966692

Simplifying
x + -6 = -7.745966692

Reorder the terms:
-6 + x = -7.745966692

Solving
-6 + x = -7.745966692

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 = -7.745966692 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.745966692 + 6
x = -7.745966692 + 6

Combine like terms: -7.745966692 + 6 = -1.745966692
x = -1.745966692

Simplifying
x = -1.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.745966692, -1.745966692}
Solution
x = {13.745966692, -1.745966692}