2n^2-10n-140=0

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Solution for 2n^2-10n-140=0 equation: 


Simplifying
2n2 + -10n + -140 = 0

Reorder the terms:
-140 + -10n + 2n2 = 0

Solving
-140 + -10n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + -5n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-70 + -5n + n2)' equal to zero and attempt to solve:

Simplifying
-70 + -5n + n2 = 0

Solving
-70 + -5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -5n + 70 + n2 = 0 + 70

Reorder the terms:
-70 + 70 + -5n + n2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -5n + n2 = 0 + 70
-5n + n2 = 0 + 70

Combine like terms: 0 + 70 = 70
-5n + n2 = 70

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 = 70 + 6.25

Reorder the terms:
6.25 + -5n + n2 = 70 + 6.25

Combine like terms: 70 + 6.25 = 76.25
6.25 + -5n + n2 = 76.25

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(n + -2.5) equal to 8.732124598 and -8.732124598.


Subproblem 1
n + -2.5 = 8.732124598

Simplifying
n + -2.5 = 8.732124598

Reorder the terms:
-2.5 + n = 8.732124598

Solving
-2.5 + n = 8.732124598

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 = 8.732124598 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 8.732124598 + 2.5
n = 8.732124598 + 2.5

Combine like terms: 8.732124598 + 2.5 = 11.232124598
n = 11.232124598

Simplifying
n = 11.232124598


Subproblem 2
n + -2.5 = -8.732124598

Simplifying
n + -2.5 = -8.732124598

Reorder the terms:
-2.5 + n = -8.732124598

Solving
-2.5 + n = -8.732124598

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 = -8.732124598 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -8.732124598 + 2.5
n = -8.732124598 + 2.5

Combine like terms: -8.732124598 + 2.5 = -6.232124598
n = -6.232124598

Simplifying
n = -6.232124598


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {11.232124598, -6.232124598}
Solution
n = {11.232124598, -6.232124598}

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