5X^2+25X+-25=0

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Solution for 5X^2+25X+-25=0 equation: 


Simplifying
5X2 + 25X + -25 = 0

Reorder the terms:
-25 + 25X + 5X2 = 0

Solving
-25 + 25X + 5X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 5X + X2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + 5X + X2)' equal to zero and attempt to solve:

Simplifying
-5 + 5X + X2 = 0

Solving
-5 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5X + 5 + X2 = 0 + 5

Reorder the terms:
-5 + 5 + 5X + X2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 5X + X2 = 0 + 5
5X + X2 = 0 + 5

Combine like terms: 0 + 5 = 5
5X + X2 = 5

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 = 5 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5X + X2 = 11.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(X + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
X + 2.5 = 3.354101966

Simplifying
X + 2.5 = 3.354101966

Reorder the terms:
2.5 + X = 3.354101966

Solving
2.5 + X = 3.354101966

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 = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 3.354101966 + -2.5
X = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
X = 0.854101966

Simplifying
X = 0.854101966


Subproblem 2
X + 2.5 = -3.354101966

Simplifying
X + 2.5 = -3.354101966

Reorder the terms:
2.5 + X = -3.354101966

Solving
2.5 + X = -3.354101966

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 = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -3.354101966 + -2.5
X = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
X = -5.854101966

Simplifying
X = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.854101966, -5.854101966}
Solution
X = {0.854101966, -5.854101966}

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