-2x^2+12x+36=0

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Solution for -2x^2+12x+36=0 equation: 


Simplifying
-2x2 + 12x + 36 = 0

Reorder the terms:
36 + 12x + -2x2 = 0

Solving
36 + 12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 6x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + 6x + -1x2 = 0

Solving
18 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + -6x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -6x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -6x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6x + x2 = 0 + 18
-6x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-6x + x2 = 18

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 = 18 + 9

Reorder the terms:
9 + -6x + x2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + -6x + x2 = 27

Factor a perfect square on the left side:
(x + -3)(x + -3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -3) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + -3 = 5.196152423

Simplifying
x + -3 = 5.196152423

Reorder the terms:
-3 + x = 5.196152423

Solving
-3 + x = 5.196152423

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 = 5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.196152423 + 3
x = 5.196152423 + 3

Combine like terms: 5.196152423 + 3 = 8.196152423
x = 8.196152423

Simplifying
x = 8.196152423


Subproblem 2
x + -3 = -5.196152423

Simplifying
x + -3 = -5.196152423

Reorder the terms:
-3 + x = -5.196152423

Solving
-3 + x = -5.196152423

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 = -5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.196152423 + 3
x = -5.196152423 + 3

Combine like terms: -5.196152423 + 3 = -2.196152423
x = -2.196152423

Simplifying
x = -2.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.196152423, -2.196152423}
Solution
x = {8.196152423, -2.196152423}

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