10x^2+250x-625=0

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Solution for 10x^2+250x-625=0 equation: 


Simplifying
10x2 + 250x + -625 = 0

Reorder the terms:
-625 + 250x + 10x2 = 0

Solving
-625 + 250x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-125 + 50x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-125 + 50x + 2x2)' equal to zero and attempt to solve:

Simplifying
-125 + 50x + 2x2 = 0

Solving
-125 + 50x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-62.5 + 25x + x2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + 25x + 62.5 + x2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + 25x + x2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + 25x + x2 = 0 + 62.5
25x + x2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
25x + x2 = 62.5

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 = 62.5 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 62.5 + 156.25

Combine like terms: 62.5 + 156.25 = 218.75
156.25 + 25x + x2 = 218.75

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 218.75

Calculate the square root of the right side: 14.790199458

Break this problem into two subproblems by setting 
(x + 12.5) equal to 14.790199458 and -14.790199458.


Subproblem 1
x + 12.5 = 14.790199458

Simplifying
x + 12.5 = 14.790199458

Reorder the terms:
12.5 + x = 14.790199458

Solving
12.5 + x = 14.790199458

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 = 14.790199458 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 14.790199458 + -12.5
x = 14.790199458 + -12.5

Combine like terms: 14.790199458 + -12.5 = 2.290199458
x = 2.290199458

Simplifying
x = 2.290199458


Subproblem 2
x + 12.5 = -14.790199458

Simplifying
x + 12.5 = -14.790199458

Reorder the terms:
12.5 + x = -14.790199458

Solving
12.5 + x = -14.790199458

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 = -14.790199458 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -14.790199458 + -12.5
x = -14.790199458 + -12.5

Combine like terms: -14.790199458 + -12.5 = -27.290199458
x = -27.290199458

Simplifying
x = -27.290199458


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.290199458, -27.290199458}
Solution
x = {2.290199458, -27.290199458}

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