4x^2-132x+216=0

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Solution for 4x^2-132x+216=0 equation: 


Simplifying
4x2 + -132x + 216 = 0

Reorder the terms:
216 + -132x + 4x2 = 0

Solving
216 + -132x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(54 + -33x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(54 + -33x + x2)' equal to zero and attempt to solve:

Simplifying
54 + -33x + x2 = 0

Solving
54 + -33x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -33x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + -33x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -33x + x2 = 0 + -54
-33x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
-33x + x2 = -54

The x term is -33x.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33x + 272.25 + x2 = -54 + 272.25

Reorder the terms:
272.25 + -33x + x2 = -54 + 272.25

Combine like terms: -54 + 272.25 = 218.25
272.25 + -33x + x2 = 218.25

Factor a perfect square on the left side:
(x + -16.5)(x + -16.5) = 218.25

Calculate the square root of the right side: 14.773286703

Break this problem into two subproblems by setting 
(x + -16.5) equal to 14.773286703 and -14.773286703.


Subproblem 1
x + -16.5 = 14.773286703

Simplifying
x + -16.5 = 14.773286703

Reorder the terms:
-16.5 + x = 14.773286703

Solving
-16.5 + x = 14.773286703

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = 14.773286703 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = 14.773286703 + 16.5
x = 14.773286703 + 16.5

Combine like terms: 14.773286703 + 16.5 = 31.273286703
x = 31.273286703

Simplifying
x = 31.273286703


Subproblem 2
x + -16.5 = -14.773286703

Simplifying
x + -16.5 = -14.773286703

Reorder the terms:
-16.5 + x = -14.773286703

Solving
-16.5 + x = -14.773286703

Solving for variable 'x'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + x = -14.773286703 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + x = -14.773286703 + 16.5
x = -14.773286703 + 16.5

Combine like terms: -14.773286703 + 16.5 = 1.726713297
x = 1.726713297

Simplifying
x = 1.726713297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.273286703, 1.726713297}
Solution
x = {31.273286703, 1.726713297}

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