f(f+2)=56

Solution for f(f+2)=56 equation:

Simplifying
f(f + 2) = 56

Reorder the terms:
f(2 + f) = 56
(2 * f + f * f) = 56
(2f + f2) = 56

Solving
2f + f2 = 56

Solving for variable 'f'.

Reorder the terms:
-56 + 2f + f2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 2f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 2f + 56 + f2 = 0 + 56

Reorder the terms:
-56 + 56 + 2f + f2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 2f + f2 = 0 + 56
2f + f2 = 0 + 56

Combine like terms: 0 + 56 = 56
2f + f2 = 56

The f term is 2f.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2f + 1 + f2 = 56 + 1

Reorder the terms:
1 + 2f + f2 = 56 + 1

Combine like terms: 56 + 1 = 57
1 + 2f + f2 = 57

Factor a perfect square on the left side:
(f + 1)(f + 1) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(f + 1) equal to 7.549834435 and -7.549834435.

Subproblem 1
f + 1 = 7.549834435

Simplifying
f + 1 = 7.549834435

Reorder the terms:
1 + f = 7.549834435

Solving
1 + f = 7.549834435

Solving for variable 'f'.

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

Add '-1' to each side of the equation.
1 + -1 + f = 7.549834435 + -1

Combine like terms: 1 + -1 = 0
0 + f = 7.549834435 + -1
f = 7.549834435 + -1

Combine like terms: 7.549834435 + -1 = 6.549834435
f = 6.549834435

Simplifying
f = 6.549834435

Subproblem 2
f + 1 = -7.549834435

Simplifying
f + 1 = -7.549834435

Reorder the terms:
1 + f = -7.549834435

Solving
1 + f = -7.549834435

Solving for variable 'f'.

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

Add '-1' to each side of the equation.
1 + -1 + f = -7.549834435 + -1

Combine like terms: 1 + -1 = 0
0 + f = -7.549834435 + -1
f = -7.549834435 + -1

Combine like terms: -7.549834435 + -1 = -8.549834435
f = -8.549834435

Simplifying
f = -8.549834435

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {6.549834435, -8.549834435}