x^2+2.5x-125=0

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Solution for x^2+2.5x-125=0 equation: 


Simplifying
x2 + 2.5x + -125 = 0

Reorder the terms:
-125 + 2.5x + x2 = 0

Solving
-125 + 2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 2.5x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 2.5x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 2.5x + x2 = 0 + 125
2.5x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
2.5x + x2 = 125

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 125 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 125 + 1.5625

Combine like terms: 125 + 1.5625 = 126.5625
1.5625 + 2.5x + x2 = 126.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 126.5625

Calculate the square root of the right side: 11.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 11.25 and -11.25.


Subproblem 1
x + 1.25 = 11.25

Simplifying
x + 1.25 = 11.25

Reorder the terms:
1.25 + x = 11.25

Solving
1.25 + x = 11.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 11.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 11.25 + -1.25
x = 11.25 + -1.25

Combine like terms: 11.25 + -1.25 = 10
x = 10

Simplifying
x = 10


Subproblem 2
x + 1.25 = -11.25

Simplifying
x + 1.25 = -11.25

Reorder the terms:
1.25 + x = -11.25

Solving
1.25 + x = -11.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -11.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -11.25 + -1.25
x = -11.25 + -1.25

Combine like terms: -11.25 + -1.25 = -12.5
x = -12.5

Simplifying
x = -12.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -12.5}

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