2f^2-32f-82=0

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Solution for 2f^2-32f-82=0 equation: 


Simplifying
2f2 + -32f + -82 = 0

Reorder the terms:
-82 + -32f + 2f2 = 0

Solving
-82 + -32f + 2f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + -16f + f2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + -16f + f2)' equal to zero and attempt to solve:

Simplifying
-41 + -16f + f2 = 0

Solving
-41 + -16f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -16f + 41 + f2 = 0 + 41

Reorder the terms:
-41 + 41 + -16f + f2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -16f + f2 = 0 + 41
-16f + f2 = 0 + 41

Combine like terms: 0 + 41 = 41
-16f + f2 = 41

The f term is -16f.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16f + 64 + f2 = 41 + 64

Reorder the terms:
64 + -16f + f2 = 41 + 64

Combine like terms: 41 + 64 = 105
64 + -16f + f2 = 105

Factor a perfect square on the left side:
(f + -8)(f + -8) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(f + -8) equal to 10.246950766 and -10.246950766.


Subproblem 1
f + -8 = 10.246950766

Simplifying
f + -8 = 10.246950766

Reorder the terms:
-8 + f = 10.246950766

Solving
-8 + f = 10.246950766

Solving for variable 'f'.

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

Add '8' to each side of the equation.
-8 + 8 + f = 10.246950766 + 8

Combine like terms: -8 + 8 = 0
0 + f = 10.246950766 + 8
f = 10.246950766 + 8

Combine like terms: 10.246950766 + 8 = 18.246950766
f = 18.246950766

Simplifying
f = 18.246950766


Subproblem 2
f + -8 = -10.246950766

Simplifying
f + -8 = -10.246950766

Reorder the terms:
-8 + f = -10.246950766

Solving
-8 + f = -10.246950766

Solving for variable 'f'.

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

Add '8' to each side of the equation.
-8 + 8 + f = -10.246950766 + 8

Combine like terms: -8 + 8 = 0
0 + f = -10.246950766 + 8
f = -10.246950766 + 8

Combine like terms: -10.246950766 + 8 = -2.246950766
f = -2.246950766

Simplifying
f = -2.246950766


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {18.246950766, -2.246950766}
Solution
f = {18.246950766, -2.246950766}

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