25x^2-8x-64=0

Solution for 25x^2-8x-64=0 equation:

Simplifying
25x2 + -8x + -64 = 0

Reorder the terms:
-64 + -8x + 25x2 = 0

Solving
-64 + -8x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-2.56 + -0.32x + x2 = 0

Move the constant term to the right:

Add '2.56' to each side of the equation.
-2.56 + -0.32x + 2.56 + x2 = 0 + 2.56

Reorder the terms:
-2.56 + 2.56 + -0.32x + x2 = 0 + 2.56

Combine like terms: -2.56 + 2.56 = 0.00
0.00 + -0.32x + x2 = 0 + 2.56
-0.32x + x2 = 0 + 2.56

Combine like terms: 0 + 2.56 = 2.56
-0.32x + x2 = 2.56

The x term is -0.32x.  Take half its coefficient (-0.16).
Square it (0.0256) and add it to both sides.

Add '0.0256' to each side of the equation.
-0.32x + 0.0256 + x2 = 2.56 + 0.0256

Reorder the terms:
0.0256 + -0.32x + x2 = 2.56 + 0.0256

Combine like terms: 2.56 + 0.0256 = 2.5856
0.0256 + -0.32x + x2 = 2.5856

Factor a perfect square on the left side:
(x + -0.16)(x + -0.16) = 2.5856

Calculate the square root of the right side: 1.607980099

Break this problem into two subproblems by setting 
(x + -0.16) equal to 1.607980099 and -1.607980099.

Subproblem 1
x + -0.16 = 1.607980099

Simplifying
x + -0.16 = 1.607980099

Reorder the terms:
-0.16 + x = 1.607980099

Solving
-0.16 + x = 1.607980099

Solving for variable 'x'.

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

Add '0.16' to each side of the equation.
-0.16 + 0.16 + x = 1.607980099 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + x = 1.607980099 + 0.16
x = 1.607980099 + 0.16

Combine like terms: 1.607980099 + 0.16 = 1.767980099
x = 1.767980099

Simplifying
x = 1.767980099

Subproblem 2
x + -0.16 = -1.607980099

Simplifying
x + -0.16 = -1.607980099

Reorder the terms:
-0.16 + x = -1.607980099

Solving
-0.16 + x = -1.607980099

Solving for variable 'x'.

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

Add '0.16' to each side of the equation.
-0.16 + 0.16 + x = -1.607980099 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + x = -1.607980099 + 0.16
x = -1.607980099 + 0.16

Combine like terms: -1.607980099 + 0.16 = -1.447980099
x = -1.447980099

Simplifying
x = -1.447980099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.767980099, -1.447980099}