2x^2-10x-108=0

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Solution for 2x^2-10x-108=0 equation: 


Simplifying
2x2 + -10x + -108 = 0

Reorder the terms:
-108 + -10x + 2x2 = 0

Solving
-108 + -10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-54 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-54 + -5x + x2 = 0

Solving
-54 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -5x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -5x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -5x + x2 = 0 + 54
-5x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-5x + x2 = 54

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 54 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 54 + 6.25

Combine like terms: 54 + 6.25 = 60.25
6.25 + -5x + x2 = 60.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
x + -2.5 = 7.762087348

Simplifying
x + -2.5 = 7.762087348

Reorder the terms:
-2.5 + x = 7.762087348

Solving
-2.5 + x = 7.762087348

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.762087348 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.762087348 + 2.5
x = 7.762087348 + 2.5

Combine like terms: 7.762087348 + 2.5 = 10.262087348
x = 10.262087348

Simplifying
x = 10.262087348


Subproblem 2
x + -2.5 = -7.762087348

Simplifying
x + -2.5 = -7.762087348

Reorder the terms:
-2.5 + x = -7.762087348

Solving
-2.5 + x = -7.762087348

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.762087348 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.762087348 + 2.5
x = -7.762087348 + 2.5

Combine like terms: -7.762087348 + 2.5 = -5.262087348
x = -5.262087348

Simplifying
x = -5.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.262087348, -5.262087348}
Solution
x = {10.262087348, -5.262087348}

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