x^2+25x-125=0

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


Simplifying
x2 + 25x + -125 = 0

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

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

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

Combine like terms: -125 + 125 = 0
0 + 25x + x2 = 0 + 125
25x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
25x + x2 = 125

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 125 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 125 + 156.25

Combine like terms: 125 + 156.25 = 281.25
156.25 + 25x + x2 = 281.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 281.25

Calculate the square root of the right side: 16.770509831

Break this problem into two subproblems by setting 
(x + 12.5) equal to 16.770509831 and -16.770509831.


Subproblem 1
x + 12.5 = 16.770509831

Simplifying
x + 12.5 = 16.770509831

Reorder the terms:
12.5 + x = 16.770509831

Solving
12.5 + x = 16.770509831

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 16.770509831 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 16.770509831 + -12.5
x = 16.770509831 + -12.5

Combine like terms: 16.770509831 + -12.5 = 4.270509831
x = 4.270509831

Simplifying
x = 4.270509831


Subproblem 2
x + 12.5 = -16.770509831

Simplifying
x + 12.5 = -16.770509831

Reorder the terms:
12.5 + x = -16.770509831

Solving
12.5 + x = -16.770509831

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -16.770509831 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -16.770509831 + -12.5
x = -16.770509831 + -12.5

Combine like terms: -16.770509831 + -12.5 = -29.270509831
x = -29.270509831

Simplifying
x = -29.270509831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.270509831, -29.270509831}

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