8x^2-144x+64=0

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Solution for 8x^2-144x+64=0 equation: 


Simplifying
8x2 + -144x + 64 = 0

Reorder the terms:
64 + -144x + 8x2 = 0

Solving
64 + -144x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + -18x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(8 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -18x + x2 = 0

Solving
8 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -18x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -18x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -18x + x2 = 0 + -8
-18x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-18x + x2 = -8

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -8 + 81

Reorder the terms:
81 + -18x + x2 = -8 + 81

Combine like terms: -8 + 81 = 73
81 + -18x + x2 = 73

Factor a perfect square on the left side:
(x + -9)(x + -9) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + -9) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + -9 = 8.544003745

Simplifying
x + -9 = 8.544003745

Reorder the terms:
-9 + x = 8.544003745

Solving
-9 + x = 8.544003745

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 8.544003745 + 9

Combine like terms: -9 + 9 = 0
0 + x = 8.544003745 + 9
x = 8.544003745 + 9

Combine like terms: 8.544003745 + 9 = 17.544003745
x = 17.544003745

Simplifying
x = 17.544003745


Subproblem 2
x + -9 = -8.544003745

Simplifying
x + -9 = -8.544003745

Reorder the terms:
-9 + x = -8.544003745

Solving
-9 + x = -8.544003745

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -8.544003745 + 9

Combine like terms: -9 + 9 = 0
0 + x = -8.544003745 + 9
x = -8.544003745 + 9

Combine like terms: -8.544003745 + 9 = 0.455996255
x = 0.455996255

Simplifying
x = 0.455996255


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.544003745, 0.455996255}
Solution
x = {17.544003745, 0.455996255}

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