4x^2-66x-144=0

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Solution for 4x^2-66x-144=0 equation: 


Simplifying
4x2 + -66x + -144 = 0

Reorder the terms:
-144 + -66x + 4x2 = 0

Solving
-144 + -66x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -33x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-72 + -33x + 2x2)' equal to zero and attempt to solve:

Simplifying
-72 + -33x + 2x2 = 0

Solving
-72 + -33x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-36 + -16.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -16.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -16.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -16.5x + x2 = 0 + 36
-16.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-16.5x + x2 = 36

The x term is -16.5x.  Take half its coefficient (-8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
-16.5x + 68.0625 + x2 = 36 + 68.0625

Reorder the terms:
68.0625 + -16.5x + x2 = 36 + 68.0625

Combine like terms: 36 + 68.0625 = 104.0625
68.0625 + -16.5x + x2 = 104.0625

Factor a perfect square on the left side:
(x + -8.25)(x + -8.25) = 104.0625

Calculate the square root of the right side: 10.201102882

Break this problem into two subproblems by setting 
(x + -8.25) equal to 10.201102882 and -10.201102882.


Subproblem 1
x + -8.25 = 10.201102882

Simplifying
x + -8.25 = 10.201102882

Reorder the terms:
-8.25 + x = 10.201102882

Solving
-8.25 + x = 10.201102882

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = 10.201102882 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = 10.201102882 + 8.25
x = 10.201102882 + 8.25

Combine like terms: 10.201102882 + 8.25 = 18.451102882
x = 18.451102882

Simplifying
x = 18.451102882


Subproblem 2
x + -8.25 = -10.201102882

Simplifying
x + -8.25 = -10.201102882

Reorder the terms:
-8.25 + x = -10.201102882

Solving
-8.25 + x = -10.201102882

Solving for variable 'x'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + x = -10.201102882 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + x = -10.201102882 + 8.25
x = -10.201102882 + 8.25

Combine like terms: -10.201102882 + 8.25 = -1.951102882
x = -1.951102882

Simplifying
x = -1.951102882


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.451102882, -1.951102882}
Solution
x = {18.451102882, -1.951102882}

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