x^2+25x-500=0

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Solution for x^2+25x-500=0 equation: 


Simplifying
x2 + 25x + -500 = 0

Reorder the terms:
-500 + 25x + x2 = 0

Solving
-500 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 25x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 25x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 25x + x2 = 0 + 500
25x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
25x + x2 = 500

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 = 500 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 500 + 156.25

Combine like terms: 500 + 156.25 = 656.25
156.25 + 25x + x2 = 656.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 656.25

Calculate the square root of the right side: 25.617376915

Break this problem into two subproblems by setting 
(x + 12.5) equal to 25.617376915 and -25.617376915.


Subproblem 1
x + 12.5 = 25.617376915

Simplifying
x + 12.5 = 25.617376915

Reorder the terms:
12.5 + x = 25.617376915

Solving
12.5 + x = 25.617376915

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 = 25.617376915 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 25.617376915 + -12.5
x = 25.617376915 + -12.5

Combine like terms: 25.617376915 + -12.5 = 13.117376915
x = 13.117376915

Simplifying
x = 13.117376915


Subproblem 2
x + 12.5 = -25.617376915

Simplifying
x + 12.5 = -25.617376915

Reorder the terms:
12.5 + x = -25.617376915

Solving
12.5 + x = -25.617376915

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 = -25.617376915 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -25.617376915 + -12.5
x = -25.617376915 + -12.5

Combine like terms: -25.617376915 + -12.5 = -38.117376915
x = -38.117376915

Simplifying
x = -38.117376915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.117376915, -38.117376915}

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