2x^2-25x-125=0

Solution for 2x^2-25x-125=0 equation:

Simplifying
2x2 + -25x + -125 = 0

Reorder the terms:
-125 + -25x + 2x2 = 0

Solving
-125 + -25x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-62.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + -12.5x + 62.5 + x2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + -12.5x + x2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + -12.5x + x2 = 0 + 62.5
-12.5x + x2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
-12.5x + x2 = 62.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 62.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 62.5 + 39.0625

Combine like terms: 62.5 + 39.0625 = 101.5625
39.0625 + -12.5x + x2 = 101.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 101.5625

Calculate the square root of the right side: 10.077822185

Break this problem into two subproblems by setting 
(x + -6.25) equal to 10.077822185 and -10.077822185.

Subproblem 1
x + -6.25 = 10.077822185

Simplifying
x + -6.25 = 10.077822185

Reorder the terms:
-6.25 + x = 10.077822185

Solving
-6.25 + x = 10.077822185

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 10.077822185 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 10.077822185 + 6.25
x = 10.077822185 + 6.25

Combine like terms: 10.077822185 + 6.25 = 16.327822185
x = 16.327822185

Simplifying
x = 16.327822185

Subproblem 2
x + -6.25 = -10.077822185

Simplifying
x + -6.25 = -10.077822185

Reorder the terms:
-6.25 + x = -10.077822185

Solving
-6.25 + x = -10.077822185

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -10.077822185 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -10.077822185 + 6.25
x = -10.077822185 + 6.25

Combine like terms: -10.077822185 + 6.25 = -3.827822185
x = -3.827822185

Simplifying
x = -3.827822185

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.327822185, -3.827822185}