8x^2-60x-25=0

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Solution for 8x^2-60x-25=0 equation: 


Simplifying
8x2 + -60x + -25 = 0

Reorder the terms:
-25 + -60x + 8x2 = 0

Solving
-25 + -60x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-3.125 + -7.5x + x2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -7.5x + 3.125 + x2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -7.5x + x2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -7.5x + x2 = 0 + 3.125
-7.5x + x2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-7.5x + x2 = 3.125

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 3.125 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 3.125 + 14.0625

Combine like terms: 3.125 + 14.0625 = 17.1875
14.0625 + -7.5x + x2 = 17.1875

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 17.1875

Calculate the square root of the right side: 4.145780988

Break this problem into two subproblems by setting 
(x + -3.75) equal to 4.145780988 and -4.145780988.


Subproblem 1
x + -3.75 = 4.145780988

Simplifying
x + -3.75 = 4.145780988

Reorder the terms:
-3.75 + x = 4.145780988

Solving
-3.75 + x = 4.145780988

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 4.145780988 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 4.145780988 + 3.75
x = 4.145780988 + 3.75

Combine like terms: 4.145780988 + 3.75 = 7.895780988
x = 7.895780988

Simplifying
x = 7.895780988


Subproblem 2
x + -3.75 = -4.145780988

Simplifying
x + -3.75 = -4.145780988

Reorder the terms:
-3.75 + x = -4.145780988

Solving
-3.75 + x = -4.145780988

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -4.145780988 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -4.145780988 + 3.75
x = -4.145780988 + 3.75

Combine like terms: -4.145780988 + 3.75 = -0.395780988
x = -0.395780988

Simplifying
x = -0.395780988


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.895780988, -0.395780988}

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