f^2+8f-37=0

Solution for f^2+8f-37=0 equation:

Simplifying
f2 + 8f + -37 = 0

Reorder the terms:
-37 + 8f + f2 = 0

Solving
-37 + 8f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 8f + 37 + f2 = 0 + 37

Reorder the terms:
-37 + 37 + 8f + f2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 8f + f2 = 0 + 37
8f + f2 = 0 + 37

Combine like terms: 0 + 37 = 37
8f + f2 = 37

The f term is 8f.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8f + 16 + f2 = 37 + 16

Reorder the terms:
16 + 8f + f2 = 37 + 16

Combine like terms: 37 + 16 = 53
16 + 8f + f2 = 53

Factor a perfect square on the left side:
(f + 4)(f + 4) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(f + 4) equal to 7.280109889 and -7.280109889.

Subproblem 1
f + 4 = 7.280109889

Simplifying
f + 4 = 7.280109889

Reorder the terms:
4 + f = 7.280109889

Solving
4 + f = 7.280109889

Solving for variable 'f'.

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

Add '-4' to each side of the equation.
4 + -4 + f = 7.280109889 + -4

Combine like terms: 4 + -4 = 0
0 + f = 7.280109889 + -4
f = 7.280109889 + -4

Combine like terms: 7.280109889 + -4 = 3.280109889
f = 3.280109889

Simplifying
f = 3.280109889

Subproblem 2
f + 4 = -7.280109889

Simplifying
f + 4 = -7.280109889

Reorder the terms:
4 + f = -7.280109889

Solving
4 + f = -7.280109889

Solving for variable 'f'.

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

Add '-4' to each side of the equation.
4 + -4 + f = -7.280109889 + -4

Combine like terms: 4 + -4 = 0
0 + f = -7.280109889 + -4
f = -7.280109889 + -4

Combine like terms: -7.280109889 + -4 = -11.280109889
f = -11.280109889

Simplifying
f = -11.280109889

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {3.280109889, -11.280109889}