6x^2-96x+48=0

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Solution for 6x^2-96x+48=0 equation: 


Simplifying
6x2 + -96x + 48 = 0

Reorder the terms:
48 + -96x + 6x2 = 0

Solving
48 + -96x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -16x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(8 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -16x + x2 = 0

Solving
8 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -16x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -16x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -16x + x2 = 0 + -8
-16x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-16x + x2 = -8

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 = -8 + 64

Reorder the terms:
64 + -16x + x2 = -8 + 64

Combine like terms: -8 + 64 = 56
64 + -16x + x2 = 56

Factor a perfect square on the left side:
(x + -8)(x + -8) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -8) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + -8 = 7.483314774

Simplifying
x + -8 = 7.483314774

Reorder the terms:
-8 + x = 7.483314774

Solving
-8 + x = 7.483314774

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 = 7.483314774 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.483314774 + 8
x = 7.483314774 + 8

Combine like terms: 7.483314774 + 8 = 15.483314774
x = 15.483314774

Simplifying
x = 15.483314774


Subproblem 2
x + -8 = -7.483314774

Simplifying
x + -8 = -7.483314774

Reorder the terms:
-8 + x = -7.483314774

Solving
-8 + x = -7.483314774

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 = -7.483314774 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.483314774 + 8
x = -7.483314774 + 8

Combine like terms: -7.483314774 + 8 = 0.516685226
x = 0.516685226

Simplifying
x = 0.516685226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.483314774, 0.516685226}
Solution
x = {15.483314774, 0.516685226}

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