f^2-8f-39=0

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Solution for f^2-8f-39=0 equation: 


Simplifying
f2 + -8f + -39 = 0

Reorder the terms:
-39 + -8f + f2 = 0

Solving
-39 + -8f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -8f + 39 + f2 = 0 + 39

Reorder the terms:
-39 + 39 + -8f + f2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -8f + f2 = 0 + 39
-8f + f2 = 0 + 39

Combine like terms: 0 + 39 = 39
-8f + f2 = 39

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 = 39 + 16

Reorder the terms:
16 + -8f + f2 = 39 + 16

Combine like terms: 39 + 16 = 55
16 + -8f + f2 = 55

Factor a perfect square on the left side:
(f + -4)(f + -4) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(f + -4) equal to 7.416198487 and -7.416198487.


Subproblem 1
f + -4 = 7.416198487

Simplifying
f + -4 = 7.416198487

Reorder the terms:
-4 + f = 7.416198487

Solving
-4 + f = 7.416198487

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 = 7.416198487 + 4

Combine like terms: -4 + 4 = 0
0 + f = 7.416198487 + 4
f = 7.416198487 + 4

Combine like terms: 7.416198487 + 4 = 11.416198487
f = 11.416198487

Simplifying
f = 11.416198487


Subproblem 2
f + -4 = -7.416198487

Simplifying
f + -4 = -7.416198487

Reorder the terms:
-4 + f = -7.416198487

Solving
-4 + f = -7.416198487

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 = -7.416198487 + 4

Combine like terms: -4 + 4 = 0
0 + f = -7.416198487 + 4
f = -7.416198487 + 4

Combine like terms: -7.416198487 + 4 = -3.416198487
f = -3.416198487

Simplifying
f = -3.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {11.416198487, -3.416198487}

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