x^2+12.5x-8=0

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Solution for x^2+12.5x-8=0 equation: 


Simplifying
x2 + 12.5x + -8 = 0

Reorder the terms:
-8 + 12.5x + x2 = 0

Solving
-8 + 12.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 12.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 12.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 12.5x + x2 = 0 + 8
12.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
12.5x + x2 = 8

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 = 8 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 8 + 39.0625

Combine like terms: 8 + 39.0625 = 47.0625
39.0625 + 12.5x + x2 = 47.0625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 47.0625

Calculate the square root of the right side: 6.860211367

Break this problem into two subproblems by setting 
(x + 6.25) equal to 6.860211367 and -6.860211367.


Subproblem 1
x + 6.25 = 6.860211367

Simplifying
x + 6.25 = 6.860211367

Reorder the terms:
6.25 + x = 6.860211367

Solving
6.25 + x = 6.860211367

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 = 6.860211367 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 6.860211367 + -6.25
x = 6.860211367 + -6.25

Combine like terms: 6.860211367 + -6.25 = 0.610211367
x = 0.610211367

Simplifying
x = 0.610211367


Subproblem 2
x + 6.25 = -6.860211367

Simplifying
x + 6.25 = -6.860211367

Reorder the terms:
6.25 + x = -6.860211367

Solving
6.25 + x = -6.860211367

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 = -6.860211367 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -6.860211367 + -6.25
x = -6.860211367 + -6.25

Combine like terms: -6.860211367 + -6.25 = -13.110211367
x = -13.110211367

Simplifying
x = -13.110211367


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.610211367, -13.110211367}

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