n^2+10n-30=0

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Solution for n^2+10n-30=0 equation: 


Simplifying
n2 + 10n + -30 = 0

Reorder the terms:
-30 + 10n + n2 = 0

Solving
-30 + 10n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 10n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + 10n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 10n + n2 = 0 + 30
10n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
10n + n2 = 30

The n term is 10n.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10n + 25 + n2 = 30 + 25

Reorder the terms:
25 + 10n + n2 = 30 + 25

Combine like terms: 30 + 25 = 55
25 + 10n + n2 = 55

Factor a perfect square on the left side:
(n + 5)(n + 5) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(n + 5) equal to 7.416198487 and -7.416198487.


Subproblem 1
n + 5 = 7.416198487

Simplifying
n + 5 = 7.416198487

Reorder the terms:
5 + n = 7.416198487

Solving
5 + n = 7.416198487

Solving for variable 'n'.

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

Add '-5' to each side of the equation.
5 + -5 + n = 7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + n = 7.416198487 + -5
n = 7.416198487 + -5

Combine like terms: 7.416198487 + -5 = 2.416198487
n = 2.416198487

Simplifying
n = 2.416198487


Subproblem 2
n + 5 = -7.416198487

Simplifying
n + 5 = -7.416198487

Reorder the terms:
5 + n = -7.416198487

Solving
5 + n = -7.416198487

Solving for variable 'n'.

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

Add '-5' to each side of the equation.
5 + -5 + n = -7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + n = -7.416198487 + -5
n = -7.416198487 + -5

Combine like terms: -7.416198487 + -5 = -12.416198487
n = -12.416198487

Simplifying
n = -12.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.416198487, -12.416198487}

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