2f^2+f-20=0

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


Simplifying
2f2 + f + -20 = 0

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

Solving
-20 + f + 2f2 = 0

Solving for variable 'f'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-10 + 0.5f + f2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 0.5f + 10 + f2 = 0 + 10

Reorder the terms:
-10 + 10 + 0.5f + f2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 0.5f + f2 = 0 + 10
0.5f + f2 = 0 + 10

Combine like terms: 0 + 10 = 10
0.5f + 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.
0.5f + 0.25 + f2 = 10 + 0.25

Reorder the terms:
0.25 + 0.5f + f2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + 0.5f + 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}

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