2x^2-60x+108=0

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Solution for 2x^2-60x+108=0 equation: 


Simplifying
2x2 + -60x + 108 = 0

Reorder the terms:
108 + -60x + 2x2 = 0

Solving
108 + -60x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(54 + -30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(54 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
54 + -30x + x2 = 0

Solving
54 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -30x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + -30x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -30x + x2 = 0 + -54
-30x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
-30x + x2 = -54

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -54 + 225

Reorder the terms:
225 + -30x + x2 = -54 + 225

Combine like terms: -54 + 225 = 171
225 + -30x + x2 = 171

Factor a perfect square on the left side:
(x + -15)(x + -15) = 171

Calculate the square root of the right side: 13.076696831

Break this problem into two subproblems by setting 
(x + -15) equal to 13.076696831 and -13.076696831.


Subproblem 1
x + -15 = 13.076696831

Simplifying
x + -15 = 13.076696831

Reorder the terms:
-15 + x = 13.076696831

Solving
-15 + x = 13.076696831

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 13.076696831 + 15

Combine like terms: -15 + 15 = 0
0 + x = 13.076696831 + 15
x = 13.076696831 + 15

Combine like terms: 13.076696831 + 15 = 28.076696831
x = 28.076696831

Simplifying
x = 28.076696831


Subproblem 2
x + -15 = -13.076696831

Simplifying
x + -15 = -13.076696831

Reorder the terms:
-15 + x = -13.076696831

Solving
-15 + x = -13.076696831

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -13.076696831 + 15

Combine like terms: -15 + 15 = 0
0 + x = -13.076696831 + 15
x = -13.076696831 + 15

Combine like terms: -13.076696831 + 15 = 1.923303169
x = 1.923303169

Simplifying
x = 1.923303169


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.076696831, 1.923303169}
Solution
x = {28.076696831, 1.923303169}

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