2n^2+10n-50=0

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Solution for 2n^2+10n-50=0 equation:


Simplifying
2n2 + 10n + -50 = 0

Reorder the terms:
-50 + 10n + 2n2 = 0

Solving
-50 + 10n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 5n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 5n + n2)' equal to zero and attempt to solve:

Simplifying
-25 + 5n + n2 = 0

Solving
-25 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 5n + 25 + n2 = 0 + 25

Reorder the terms:
-25 + 25 + 5n + n2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 5n + n2 = 0 + 25
5n + n2 = 0 + 25

Combine like terms: 0 + 25 = 25
5n + n2 = 25

The n term is 5n.  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.
5n + 6.25 + n2 = 25 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + 5n + n2 = 31.25

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

Calculate the square root of the right side: 5.590169944

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


Subproblem 1
n + 2.5 = 5.590169944

Simplifying
n + 2.5 = 5.590169944

Reorder the terms:
2.5 + n = 5.590169944

Solving
2.5 + n = 5.590169944

Solving for variable 'n'.

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

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

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

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

Simplifying
n = 3.090169944


Subproblem 2
n + 2.5 = -5.590169944

Simplifying
n + 2.5 = -5.590169944

Reorder the terms:
2.5 + n = -5.590169944

Solving
2.5 + n = -5.590169944

Solving for variable 'n'.

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

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

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

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

Simplifying
n = -8.090169944


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

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