f(f+8)=64

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Solution for f(f+8)=64 equation: 


Simplifying
f(f + 8) = 64

Reorder the terms:
f(8 + f) = 64
(8 * f + f * f) = 64
(8f + f2) = 64

Solving
8f + f2 = 64

Solving for variable 'f'.

Reorder the terms:
-64 + 8f + f2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 8f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 8f + 64 + f2 = 0 + 64

Reorder the terms:
-64 + 64 + 8f + f2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 8f + f2 = 0 + 64
8f + f2 = 0 + 64

Combine like terms: 0 + 64 = 64
8f + f2 = 64

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 = 64 + 16

Reorder the terms:
16 + 8f + f2 = 64 + 16

Combine like terms: 64 + 16 = 80
16 + 8f + f2 = 80

Factor a perfect square on the left side:
(f + 4)(f + 4) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(f + 4) equal to 8.94427191 and -8.94427191.


Subproblem 1
f + 4 = 8.94427191

Simplifying
f + 4 = 8.94427191

Reorder the terms:
4 + f = 8.94427191

Solving
4 + f = 8.94427191

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 = 8.94427191 + -4

Combine like terms: 4 + -4 = 0
0 + f = 8.94427191 + -4
f = 8.94427191 + -4

Combine like terms: 8.94427191 + -4 = 4.94427191
f = 4.94427191

Simplifying
f = 4.94427191


Subproblem 2
f + 4 = -8.94427191

Simplifying
f + 4 = -8.94427191

Reorder the terms:
4 + f = -8.94427191

Solving
4 + f = -8.94427191

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 = -8.94427191 + -4

Combine like terms: 4 + -4 = 0
0 + f = -8.94427191 + -4
f = -8.94427191 + -4

Combine like terms: -8.94427191 + -4 = -12.94427191
f = -12.94427191

Simplifying
f = -12.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {4.94427191, -12.94427191}

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