64x^2-72x-16=0

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Solution for 64x^2-72x-16=0 equation: 


Simplifying
64x2 + -72x + -16 = 0

Reorder the terms:
-16 + -72x + 64x2 = 0

Solving
-16 + -72x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -9x + 8x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-2 + -9x + 8x2)' equal to zero and attempt to solve:

Simplifying
-2 + -9x + 8x2 = 0

Solving
-2 + -9x + 8x2 = 0

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

Divide each side by '8'.
-0.25 + -1.125x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.125x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.125x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.125x + x2 = 0 + 0.25
-1.125x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.125x + x2 = 0.25

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = 0.25 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = 0.25 + 0.31640625

Combine like terms: 0.25 + 0.31640625 = 0.56640625
0.31640625 + -1.125x + x2 = 0.56640625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 0.56640625

Calculate the square root of the right side: 0.752599661

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 0.752599661 and -0.752599661.


Subproblem 1
x + -0.5625 = 0.752599661

Simplifying
x + -0.5625 = 0.752599661

Reorder the terms:
-0.5625 + x = 0.752599661

Solving
-0.5625 + x = 0.752599661

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = 0.752599661 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = 0.752599661 + 0.5625
x = 0.752599661 + 0.5625

Combine like terms: 0.752599661 + 0.5625 = 1.315099661
x = 1.315099661

Simplifying
x = 1.315099661


Subproblem 2
x + -0.5625 = -0.752599661

Simplifying
x + -0.5625 = -0.752599661

Reorder the terms:
-0.5625 + x = -0.752599661

Solving
-0.5625 + x = -0.752599661

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = -0.752599661 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = -0.752599661 + 0.5625
x = -0.752599661 + 0.5625

Combine like terms: -0.752599661 + 0.5625 = -0.190099661
x = -0.190099661

Simplifying
x = -0.190099661


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.315099661, -0.190099661}
Solution
x = {1.315099661, -0.190099661}

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