11x^2-12x=9x^2+12x+4

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Solution for 11x^2-12x=9x^2+12x+4 equation: 


Simplifying
11x2 + -12x = 9x2 + 12x + 4

Reorder the terms:
-12x + 11x2 = 9x2 + 12x + 4

Reorder the terms:
-12x + 11x2 = 4 + 12x + 9x2

Solving
-12x + 11x2 = 4 + 12x + 9x2

Solving for variable 'x'.

Reorder the terms:
-4 + -12x + -12x + 11x2 + -9x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Combine like terms: -12x + -12x = -24x
-4 + -24x + 11x2 + -9x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Combine like terms: 11x2 + -9x2 = 2x2
-4 + -24x + 2x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Reorder the terms:
-4 + -24x + 2x2 = 4 + -4 + 12x + -12x + 9x2 + -9x2

Combine like terms: 4 + -4 = 0
-4 + -24x + 2x2 = 0 + 12x + -12x + 9x2 + -9x2
-4 + -24x + 2x2 = 12x + -12x + 9x2 + -9x2

Combine like terms: 12x + -12x = 0
-4 + -24x + 2x2 = 0 + 9x2 + -9x2
-4 + -24x + 2x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-4 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -12x + x2 = 0

Solving
-2 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -12x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -12x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -12x + x2 = 0 + 2
-12x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-12x + x2 = 2

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 = 2 + 36

Reorder the terms:
36 + -12x + x2 = 2 + 36

Combine like terms: 2 + 36 = 38
36 + -12x + x2 = 38

Factor a perfect square on the left side:
(x + -6)(x + -6) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + -6) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + -6 = 6.164414003

Simplifying
x + -6 = 6.164414003

Reorder the terms:
-6 + x = 6.164414003

Solving
-6 + x = 6.164414003

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 = 6.164414003 + 6

Combine like terms: -6 + 6 = 0
0 + x = 6.164414003 + 6
x = 6.164414003 + 6

Combine like terms: 6.164414003 + 6 = 12.164414003
x = 12.164414003

Simplifying
x = 12.164414003


Subproblem 2
x + -6 = -6.164414003

Simplifying
x + -6 = -6.164414003

Reorder the terms:
-6 + x = -6.164414003

Solving
-6 + x = -6.164414003

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 = -6.164414003 + 6

Combine like terms: -6 + 6 = 0
0 + x = -6.164414003 + 6
x = -6.164414003 + 6

Combine like terms: -6.164414003 + 6 = -0.164414003
x = -0.164414003

Simplifying
x = -0.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.164414003, -0.164414003}
Solution
x = {12.164414003, -0.164414003}

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