5x^2+100x-125=0

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Solution for 5x^2+100x-125=0 equation: 


Simplifying
5x2 + 100x + -125 = 0

Reorder the terms:
-125 + 100x + 5x2 = 0

Solving
-125 + 100x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-25 + 20x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-25 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + 20x + x2 = 0

Solving
-25 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 20x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 20x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 20x + x2 = 0 + 25
20x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
20x + x2 = 25

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 25 + 100

Reorder the terms:
100 + 20x + x2 = 25 + 100

Combine like terms: 25 + 100 = 125
100 + 20x + x2 = 125

Factor a perfect square on the left side:
(x + 10)(x + 10) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 10) equal to 11.180339887 and -11.180339887.


Subproblem 1
x + 10 = 11.180339887

Simplifying
x + 10 = 11.180339887

Reorder the terms:
10 + x = 11.180339887

Solving
10 + x = 11.180339887

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 11.180339887 + -10

Combine like terms: 10 + -10 = 0
0 + x = 11.180339887 + -10
x = 11.180339887 + -10

Combine like terms: 11.180339887 + -10 = 1.180339887
x = 1.180339887

Simplifying
x = 1.180339887


Subproblem 2
x + 10 = -11.180339887

Simplifying
x + 10 = -11.180339887

Reorder the terms:
10 + x = -11.180339887

Solving
10 + x = -11.180339887

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -11.180339887 + -10

Combine like terms: 10 + -10 = 0
0 + x = -11.180339887 + -10
x = -11.180339887 + -10

Combine like terms: -11.180339887 + -10 = -21.180339887
x = -21.180339887

Simplifying
x = -21.180339887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.180339887, -21.180339887}
Solution
x = {1.180339887, -21.180339887}

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