f^2+5f-105=0

Solution for f^2+5f-105=0 equation:

Simplifying
f2 + 5f + -105 = 0

Reorder the terms:
-105 + 5f + f2 = 0

Solving
-105 + 5f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 5f + 105 + f2 = 0 + 105

Reorder the terms:
-105 + 105 + 5f + f2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 5f + f2 = 0 + 105
5f + f2 = 0 + 105

Combine like terms: 0 + 105 = 105
5f + f2 = 105

The f term is 5f.  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.
5f + 6.25 + f2 = 105 + 6.25

Reorder the terms:
6.25 + 5f + f2 = 105 + 6.25

Combine like terms: 105 + 6.25 = 111.25
6.25 + 5f + f2 = 111.25

Factor a perfect square on the left side:
(f + 2.5)(f + 2.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(f + 2.5) equal to 10.547511555 and -10.547511555.

Subproblem 1
f + 2.5 = 10.547511555

Simplifying
f + 2.5 = 10.547511555

Reorder the terms:
2.5 + f = 10.547511555

Solving
2.5 + f = 10.547511555

Solving for variable 'f'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + f = 10.547511555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + f = 10.547511555 + -2.5
f = 10.547511555 + -2.5

Combine like terms: 10.547511555 + -2.5 = 8.047511555
f = 8.047511555

Simplifying
f = 8.047511555

Subproblem 2
f + 2.5 = -10.547511555

Simplifying
f + 2.5 = -10.547511555

Reorder the terms:
2.5 + f = -10.547511555

Solving
2.5 + f = -10.547511555

Solving for variable 'f'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + f = -10.547511555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + f = -10.547511555 + -2.5
f = -10.547511555 + -2.5

Combine like terms: -10.547511555 + -2.5 = -13.047511555
f = -13.047511555

Simplifying
f = -13.047511555

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {8.047511555, -13.047511555}