64x^2-144x-81=0

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Solution for 64x^2-144x-81=0 equation: 


Simplifying
64x2 + -144x + -81 = 0

Reorder the terms:
-81 + -144x + 64x2 = 0

Solving
-81 + -144x + 64x2 = 0

Solving for variable 'x'.

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

Divide each side by '64'.
-1.265625 + -2.25x + x2 = 0

Move the constant term to the right:

Add '1.265625' to each side of the equation.
-1.265625 + -2.25x + 1.265625 + x2 = 0 + 1.265625

Reorder the terms:
-1.265625 + 1.265625 + -2.25x + x2 = 0 + 1.265625

Combine like terms: -1.265625 + 1.265625 = 0.000000
0.000000 + -2.25x + x2 = 0 + 1.265625
-2.25x + x2 = 0 + 1.265625

Combine like terms: 0 + 1.265625 = 1.265625
-2.25x + x2 = 1.265625

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 = 1.265625 + 1.265625

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

Combine like terms: 1.265625 + 1.265625 = 2.53125
1.265625 + -2.25x + x2 = 2.53125

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 2.53125

Calculate the square root of the right side: 1.590990258

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.590990258 and -1.590990258.


Subproblem 1
x + -1.125 = 1.590990258

Simplifying
x + -1.125 = 1.590990258

Reorder the terms:
-1.125 + x = 1.590990258

Solving
-1.125 + x = 1.590990258

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 = 1.590990258 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.590990258 + 1.125
x = 1.590990258 + 1.125

Combine like terms: 1.590990258 + 1.125 = 2.715990258
x = 2.715990258

Simplifying
x = 2.715990258


Subproblem 2
x + -1.125 = -1.590990258

Simplifying
x + -1.125 = -1.590990258

Reorder the terms:
-1.125 + x = -1.590990258

Solving
-1.125 + x = -1.590990258

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 = -1.590990258 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.590990258 + 1.125
x = -1.590990258 + 1.125

Combine like terms: -1.590990258 + 1.125 = -0.465990258
x = -0.465990258

Simplifying
x = -0.465990258


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.715990258, -0.465990258}

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