2f^2+2f-20=0

Solution for 2f^2+2f-20=0 equation:

Simplifying
2f2 + 2f + -20 = 0

Reorder the terms:
-20 + 2f + 2f2 = 0

Solving
-20 + 2f + 2f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + f + f2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + f + f2)' equal to zero and attempt to solve:

Simplifying
-10 + f + f2 = 0

Solving
-10 + f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + f + 10 + f2 = 0 + 10

Reorder the terms:
-10 + 10 + f + f2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + f + f2 = 0 + 10
f + f2 = 0 + 10

Combine like terms: 0 + 10 = 10
f + f2 = 10

The f term is f.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
f + 0.25 + f2 = 10 + 0.25

Reorder the terms:
0.25 + f + f2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + f + f2 = 10.25

Factor a perfect square on the left side:
(f + 0.5)(f + 0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(f + 0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
f + 0.5 = 3.201562119

Simplifying
f + 0.5 = 3.201562119

Reorder the terms:
0.5 + f = 3.201562119

Solving
0.5 + f = 3.201562119

Solving for variable 'f'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + f = 3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + f = 3.201562119 + -0.5
f = 3.201562119 + -0.5

Combine like terms: 3.201562119 + -0.5 = 2.701562119
f = 2.701562119

Simplifying
f = 2.701562119

Subproblem 2
f + 0.5 = -3.201562119

Simplifying
f + 0.5 = -3.201562119

Reorder the terms:
0.5 + f = -3.201562119

Solving
0.5 + f = -3.201562119

Solving for variable 'f'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + f = -3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + f = -3.201562119 + -0.5
f = -3.201562119 + -0.5

Combine like terms: -3.201562119 + -0.5 = -3.701562119
f = -3.701562119

Simplifying
f = -3.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {2.701562119, -3.701562119}
Solution
f = {2.701562119, -3.701562119}