2x^2-48x+128=0

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Solution for 2x^2-48x+128=0 equation: 


Simplifying
2x2 + -48x + 128 = 0

Reorder the terms:
128 + -48x + 2x2 = 0

Solving
128 + -48x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(64 + -24x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(64 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
64 + -24x + x2 = 0

Solving
64 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -24x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -24x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -24x + x2 = 0 + -64
-24x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-24x + x2 = -64

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -64 + 144

Reorder the terms:
144 + -24x + x2 = -64 + 144

Combine like terms: -64 + 144 = 80
144 + -24x + x2 = 80

Factor a perfect square on the left side:
(x + -12)(x + -12) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + -12) equal to 8.94427191 and -8.94427191.


Subproblem 1
x + -12 = 8.94427191

Simplifying
x + -12 = 8.94427191

Reorder the terms:
-12 + x = 8.94427191

Solving
-12 + x = 8.94427191

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 8.94427191 + 12

Combine like terms: -12 + 12 = 0
0 + x = 8.94427191 + 12
x = 8.94427191 + 12

Combine like terms: 8.94427191 + 12 = 20.94427191
x = 20.94427191

Simplifying
x = 20.94427191


Subproblem 2
x + -12 = -8.94427191

Simplifying
x + -12 = -8.94427191

Reorder the terms:
-12 + x = -8.94427191

Solving
-12 + x = -8.94427191

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -8.94427191 + 12

Combine like terms: -12 + 12 = 0
0 + x = -8.94427191 + 12
x = -8.94427191 + 12

Combine like terms: -8.94427191 + 12 = 3.05572809
x = 3.05572809

Simplifying
x = 3.05572809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.94427191, 3.05572809}
Solution
x = {20.94427191, 3.05572809}

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