2x^2-12x-36=28

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Solution for 2x^2-12x-36=28 equation: 


Simplifying
2x2 + -12x + -36 = 28

Reorder the terms:
-36 + -12x + 2x2 = 28

Solving
-36 + -12x + 2x2 = 28

Solving for variable 'x'.

Reorder the terms:
-36 + -28 + -12x + 2x2 = 28 + -28

Combine like terms: -36 + -28 = -64
-64 + -12x + 2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-64 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-32 + -6x + x2 = 0

Solving
-32 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -6x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -6x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -6x + x2 = 0 + 32
-6x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-6x + x2 = 32

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 32 + 9

Reorder the terms:
9 + -6x + x2 = 32 + 9

Combine like terms: 32 + 9 = 41
9 + -6x + x2 = 41

Factor a perfect square on the left side:
(x + -3)(x + -3) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -3) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -3 = 6.403124237

Simplifying
x + -3 = 6.403124237

Reorder the terms:
-3 + x = 6.403124237

Solving
-3 + x = 6.403124237

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.403124237 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.403124237 + 3
x = 6.403124237 + 3

Combine like terms: 6.403124237 + 3 = 9.403124237
x = 9.403124237

Simplifying
x = 9.403124237


Subproblem 2
x + -3 = -6.403124237

Simplifying
x + -3 = -6.403124237

Reorder the terms:
-3 + x = -6.403124237

Solving
-3 + x = -6.403124237

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.403124237 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.403124237 + 3
x = -6.403124237 + 3

Combine like terms: -6.403124237 + 3 = -3.403124237
x = -3.403124237

Simplifying
x = -3.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.403124237, -3.403124237}
Solution
x = {9.403124237, -3.403124237}

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