2x^2-6x-180=0

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Solution for 2x^2-6x-180=0 equation: 


Simplifying
2x2 + -6x + -180 = 0

Reorder the terms:
-180 + -6x + 2x2 = 0

Solving
-180 + -6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + -3x + x2 = 0

Solving
-90 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -3x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -3x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -3x + x2 = 0 + 90
-3x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-3x + x2 = 90

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 90 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 90 + 2.25

Combine like terms: 90 + 2.25 = 92.25
2.25 + -3x + x2 = 92.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + -1.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + -1.5 = 9.604686356

Simplifying
x + -1.5 = 9.604686356

Reorder the terms:
-1.5 + x = 9.604686356

Solving
-1.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 9.604686356 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 9.604686356 + 1.5
x = 9.604686356 + 1.5

Combine like terms: 9.604686356 + 1.5 = 11.104686356
x = 11.104686356

Simplifying
x = 11.104686356


Subproblem 2
x + -1.5 = -9.604686356

Simplifying
x + -1.5 = -9.604686356

Reorder the terms:
-1.5 + x = -9.604686356

Solving
-1.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -9.604686356 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -9.604686356 + 1.5
x = -9.604686356 + 1.5

Combine like terms: -9.604686356 + 1.5 = -8.104686356
x = -8.104686356

Simplifying
x = -8.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.104686356, -8.104686356}
Solution
x = {11.104686356, -8.104686356}

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