2x^2-36x-162=0

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Solution for 2x^2-36x-162=0 equation: 


Simplifying
2x2 + -36x + -162 = 0

Reorder the terms:
-162 + -36x + 2x2 = 0

Solving
-162 + -36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-81 + -18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-81 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
-81 + -18x + x2 = 0

Solving
-81 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -18x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -18x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -18x + x2 = 0 + 81
-18x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-18x + x2 = 81

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 = 81 + 81

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

Combine like terms: 81 + 81 = 162
81 + -18x + x2 = 162

Factor a perfect square on the left side:
(x + -9)(x + -9) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(x + -9) equal to 12.727922061 and -12.727922061.


Subproblem 1
x + -9 = 12.727922061

Simplifying
x + -9 = 12.727922061

Reorder the terms:
-9 + x = 12.727922061

Solving
-9 + x = 12.727922061

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 = 12.727922061 + 9

Combine like terms: -9 + 9 = 0
0 + x = 12.727922061 + 9
x = 12.727922061 + 9

Combine like terms: 12.727922061 + 9 = 21.727922061
x = 21.727922061

Simplifying
x = 21.727922061


Subproblem 2
x + -9 = -12.727922061

Simplifying
x + -9 = -12.727922061

Reorder the terms:
-9 + x = -12.727922061

Solving
-9 + x = -12.727922061

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 = -12.727922061 + 9

Combine like terms: -9 + 9 = 0
0 + x = -12.727922061 + 9
x = -12.727922061 + 9

Combine like terms: -12.727922061 + 9 = -3.727922061
x = -3.727922061

Simplifying
x = -3.727922061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.727922061, -3.727922061}
Solution
x = {21.727922061, -3.727922061}

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