25x^2+125x-625=0

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Solution for 25x^2+125x-625=0 equation: 


Simplifying
25x2 + 125x + -625 = 0

Reorder the terms:
-625 + 125x + 25x2 = 0

Solving
-625 + 125x + 25x2 = 0

Solving for variable 'x'.

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

Ignore the factor 25.

Subproblem 1
Set the factor '(-25 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + 5x + x2 = 0

Solving
-25 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 5x + x2 = 0 + 25
5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
5x + x2 = 25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + 5x + x2 = 31.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
x + 2.5 = 5.590169944

Simplifying
x + 2.5 = 5.590169944

Reorder the terms:
2.5 + x = 5.590169944

Solving
2.5 + x = 5.590169944

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 5.590169944 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.590169944 + -2.5
x = 5.590169944 + -2.5

Combine like terms: 5.590169944 + -2.5 = 3.090169944
x = 3.090169944

Simplifying
x = 3.090169944


Subproblem 2
x + 2.5 = -5.590169944

Simplifying
x + 2.5 = -5.590169944

Reorder the terms:
2.5 + x = -5.590169944

Solving
2.5 + x = -5.590169944

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -5.590169944 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.590169944 + -2.5
x = -5.590169944 + -2.5

Combine like terms: -5.590169944 + -2.5 = -8.090169944
x = -8.090169944

Simplifying
x = -8.090169944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.090169944, -8.090169944}
Solution
x = {3.090169944, -8.090169944}

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