3x^2-48x-36=0

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Solution for 3x^2-48x-36=0 equation: 


Simplifying
3x2 + -48x + -36 = 0

Reorder the terms:
-36 + -48x + 3x2 = 0

Solving
-36 + -48x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -16x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-12 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + -16x + x2 = 0

Solving
-12 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -16x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -16x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -16x + x2 = 0 + 12
-16x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-16x + x2 = 12

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 12 + 64

Reorder the terms:
64 + -16x + x2 = 12 + 64

Combine like terms: 12 + 64 = 76
64 + -16x + x2 = 76

Factor a perfect square on the left side:
(x + -8)(x + -8) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -8) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + -8 = 8.717797887

Simplifying
x + -8 = 8.717797887

Reorder the terms:
-8 + x = 8.717797887

Solving
-8 + x = 8.717797887

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.717797887 + 8
x = 8.717797887 + 8

Combine like terms: 8.717797887 + 8 = 16.717797887
x = 16.717797887

Simplifying
x = 16.717797887


Subproblem 2
x + -8 = -8.717797887

Simplifying
x + -8 = -8.717797887

Reorder the terms:
-8 + x = -8.717797887

Solving
-8 + x = -8.717797887

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.717797887 + 8
x = -8.717797887 + 8

Combine like terms: -8.717797887 + 8 = -0.717797887
x = -0.717797887

Simplifying
x = -0.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.717797887, -0.717797887}
Solution
x = {16.717797887, -0.717797887}

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