2x^2-36x-136=0

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Solution for 2x^2-36x-136=0 equation: 


Simplifying
2x2 + -36x + -136 = 0

Reorder the terms:
-136 + -36x + 2x2 = 0

Solving
-136 + -36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
-68 + -18x + x2 = 0

Solving
-68 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -18x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + -18x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -18x + x2 = 0 + 68
-18x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
-18x + x2 = 68

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 68 + 81

Reorder the terms:
81 + -18x + x2 = 68 + 81

Combine like terms: 68 + 81 = 149
81 + -18x + x2 = 149

Factor a perfect square on the left side:
(x + -9)(x + -9) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(x + -9) equal to 12.206555616 and -12.206555616.


Subproblem 1
x + -9 = 12.206555616

Simplifying
x + -9 = 12.206555616

Reorder the terms:
-9 + x = 12.206555616

Solving
-9 + x = 12.206555616

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 12.206555616 + 9

Combine like terms: -9 + 9 = 0
0 + x = 12.206555616 + 9
x = 12.206555616 + 9

Combine like terms: 12.206555616 + 9 = 21.206555616
x = 21.206555616

Simplifying
x = 21.206555616


Subproblem 2
x + -9 = -12.206555616

Simplifying
x + -9 = -12.206555616

Reorder the terms:
-9 + x = -12.206555616

Solving
-9 + x = -12.206555616

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -12.206555616 + 9

Combine like terms: -9 + 9 = 0
0 + x = -12.206555616 + 9
x = -12.206555616 + 9

Combine like terms: -12.206555616 + 9 = -3.206555616
x = -3.206555616

Simplifying
x = -3.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.206555616, -3.206555616}
Solution
x = {21.206555616, -3.206555616}

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