n^2+7n-36=0

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Solution for n^2+7n-36=0 equation: 


Simplifying
n2 + 7n + -36 = 0

Reorder the terms:
-36 + 7n + n2 = 0

Solving
-36 + 7n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 7n + 36 + n2 = 0 + 36

Reorder the terms:
-36 + 36 + 7n + n2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 7n + n2 = 0 + 36
7n + n2 = 0 + 36

Combine like terms: 0 + 36 = 36
7n + n2 = 36

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 36 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 36 + 12.25

Combine like terms: 36 + 12.25 = 48.25
12.25 + 7n + n2 = 48.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(n + 3.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
n + 3.5 = 6.946221995

Simplifying
n + 3.5 = 6.946221995

Reorder the terms:
3.5 + n = 6.946221995

Solving
3.5 + n = 6.946221995

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 6.946221995 + -3.5
n = 6.946221995 + -3.5

Combine like terms: 6.946221995 + -3.5 = 3.446221995
n = 3.446221995

Simplifying
n = 3.446221995


Subproblem 2
n + 3.5 = -6.946221995

Simplifying
n + 3.5 = -6.946221995

Reorder the terms:
3.5 + n = -6.946221995

Solving
3.5 + n = -6.946221995

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -6.946221995 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -6.946221995 + -3.5
n = -6.946221995 + -3.5

Combine like terms: -6.946221995 + -3.5 = -10.446221995
n = -10.446221995

Simplifying
n = -10.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.446221995, -10.446221995}

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