n^2+37n-340=0

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Solution for n^2+37n-340=0 equation: 


Simplifying
n2 + 37n + -340 = 0

Reorder the terms:
-340 + 37n + n2 = 0

Solving
-340 + 37n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '340' to each side of the equation.
-340 + 37n + 340 + n2 = 0 + 340

Reorder the terms:
-340 + 340 + 37n + n2 = 0 + 340

Combine like terms: -340 + 340 = 0
0 + 37n + n2 = 0 + 340
37n + n2 = 0 + 340

Combine like terms: 0 + 340 = 340
37n + n2 = 340

The n term is 37n.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37n + 342.25 + n2 = 340 + 342.25

Reorder the terms:
342.25 + 37n + n2 = 340 + 342.25

Combine like terms: 340 + 342.25 = 682.25
342.25 + 37n + n2 = 682.25

Factor a perfect square on the left side:
(n + 18.5)(n + 18.5) = 682.25

Calculate the square root of the right side: 26.119915773

Break this problem into two subproblems by setting 
(n + 18.5) equal to 26.119915773 and -26.119915773.


Subproblem 1
n + 18.5 = 26.119915773

Simplifying
n + 18.5 = 26.119915773

Reorder the terms:
18.5 + n = 26.119915773

Solving
18.5 + n = 26.119915773

Solving for variable 'n'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + n = 26.119915773 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + n = 26.119915773 + -18.5
n = 26.119915773 + -18.5

Combine like terms: 26.119915773 + -18.5 = 7.619915773
n = 7.619915773

Simplifying
n = 7.619915773


Subproblem 2
n + 18.5 = -26.119915773

Simplifying
n + 18.5 = -26.119915773

Reorder the terms:
18.5 + n = -26.119915773

Solving
18.5 + n = -26.119915773

Solving for variable 'n'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + n = -26.119915773 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + n = -26.119915773 + -18.5
n = -26.119915773 + -18.5

Combine like terms: -26.119915773 + -18.5 = -44.619915773
n = -44.619915773

Simplifying
n = -44.619915773


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.619915773, -44.619915773}

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