64x^2-144x+8=0

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


Simplifying
64x2 + -144x + 8 = 0

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

Solving
8 + -144x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -18x + 8x2) = 0

Ignore the factor 8.

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

Simplifying
1 + -18x + 8x2 = 0

Solving
1 + -18x + 8x2 = 0

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

Divide each side by '8'.
0.125 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -2.25x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -2.25x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -2.25x + x2 = 0 + -0.125
-2.25x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-2.25x + x2 = -0.125

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.125 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.125 + 1.265625

Combine like terms: -0.125 + 1.265625 = 1.140625
1.265625 + -2.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.068000468 and -1.068000468.


Subproblem 1
x + -1.125 = 1.068000468

Simplifying
x + -1.125 = 1.068000468

Reorder the terms:
-1.125 + x = 1.068000468

Solving
-1.125 + x = 1.068000468

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 1.068000468 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.068000468 + 1.125
x = 1.068000468 + 1.125

Combine like terms: 1.068000468 + 1.125 = 2.193000468
x = 2.193000468

Simplifying
x = 2.193000468


Subproblem 2
x + -1.125 = -1.068000468

Simplifying
x + -1.125 = -1.068000468

Reorder the terms:
-1.125 + x = -1.068000468

Solving
-1.125 + x = -1.068000468

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -1.068000468 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.068000468 + 1.125
x = -1.068000468 + 1.125

Combine like terms: -1.068000468 + 1.125 = 0.056999532
x = 0.056999532

Simplifying
x = 0.056999532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.193000468, 0.056999532}
Solution
x = {2.193000468, 0.056999532}

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