f^2+8f+11=0

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Solution for f^2+8f+11=0 equation: 


Simplifying
f2 + 8f + 11 = 0

Reorder the terms:
11 + 8f + f2 = 0

Solving
11 + 8f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8f + -11 + f2 = 0 + -11

Reorder the terms:
11 + -11 + 8f + f2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8f + f2 = 0 + -11
8f + f2 = 0 + -11

Combine like terms: 0 + -11 = -11
8f + f2 = -11

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 = -11 + 16

Reorder the terms:
16 + 8f + f2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + 8f + f2 = 5

Factor a perfect square on the left side:
(f + 4)(f + 4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(f + 4) equal to 2.236067978 and -2.236067978.


Subproblem 1
f + 4 = 2.236067978

Simplifying
f + 4 = 2.236067978

Reorder the terms:
4 + f = 2.236067978

Solving
4 + f = 2.236067978

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 = 2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + f = 2.236067978 + -4
f = 2.236067978 + -4

Combine like terms: 2.236067978 + -4 = -1.763932022
f = -1.763932022

Simplifying
f = -1.763932022


Subproblem 2
f + 4 = -2.236067978

Simplifying
f + 4 = -2.236067978

Reorder the terms:
4 + f = -2.236067978

Solving
4 + f = -2.236067978

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 = -2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + f = -2.236067978 + -4
f = -2.236067978 + -4

Combine like terms: -2.236067978 + -4 = -6.236067978
f = -6.236067978

Simplifying
f = -6.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-1.763932022, -6.236067978}

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