4x^2-5x-64=0

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Solution for 4x^2-5x-64=0 equation: 


Simplifying
4x2 + -5x + -64 = 0

Reorder the terms:
-64 + -5x + 4x2 = 0

Solving
-64 + -5x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-16 + -1.25x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -1.25x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -1.25x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1.25x + x2 = 0 + 16
-1.25x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1.25x + x2 = 16

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 16 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 16 + 0.390625

Combine like terms: 16 + 0.390625 = 16.390625
0.390625 + -1.25x + x2 = 16.390625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 16.390625

Calculate the square root of the right side: 4.048533685

Break this problem into two subproblems by setting 
(x + -0.625) equal to 4.048533685 and -4.048533685.


Subproblem 1
x + -0.625 = 4.048533685

Simplifying
x + -0.625 = 4.048533685

Reorder the terms:
-0.625 + x = 4.048533685

Solving
-0.625 + x = 4.048533685

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 4.048533685 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 4.048533685 + 0.625
x = 4.048533685 + 0.625

Combine like terms: 4.048533685 + 0.625 = 4.673533685
x = 4.673533685

Simplifying
x = 4.673533685


Subproblem 2
x + -0.625 = -4.048533685

Simplifying
x + -0.625 = -4.048533685

Reorder the terms:
-0.625 + x = -4.048533685

Solving
-0.625 + x = -4.048533685

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -4.048533685 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -4.048533685 + 0.625
x = -4.048533685 + 0.625

Combine like terms: -4.048533685 + 0.625 = -3.423533685
x = -3.423533685

Simplifying
x = -3.423533685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.673533685, -3.423533685}

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