f^2-11f-18=0

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Solution for f^2-11f-18=0 equation: 


Simplifying
f2 + -11f + -18 = 0

Reorder the terms:
-18 + -11f + f2 = 0

Solving
-18 + -11f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -11f + 18 + f2 = 0 + 18

Reorder the terms:
-18 + 18 + -11f + f2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -11f + f2 = 0 + 18
-11f + f2 = 0 + 18

Combine like terms: 0 + 18 = 18
-11f + f2 = 18

The f term is -11f.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11f + 30.25 + f2 = 18 + 30.25

Reorder the terms:
30.25 + -11f + f2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + -11f + f2 = 48.25

Factor a perfect square on the left side:
(f + -5.5)(f + -5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(f + -5.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
f + -5.5 = 6.946221995

Simplifying
f + -5.5 = 6.946221995

Reorder the terms:
-5.5 + f = 6.946221995

Solving
-5.5 + f = 6.946221995

Solving for variable 'f'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + f = 6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + f = 6.946221995 + 5.5
f = 6.946221995 + 5.5

Combine like terms: 6.946221995 + 5.5 = 12.446221995
f = 12.446221995

Simplifying
f = 12.446221995


Subproblem 2
f + -5.5 = -6.946221995

Simplifying
f + -5.5 = -6.946221995

Reorder the terms:
-5.5 + f = -6.946221995

Solving
-5.5 + f = -6.946221995

Solving for variable 'f'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + f = -6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + f = -6.946221995 + 5.5
f = -6.946221995 + 5.5

Combine like terms: -6.946221995 + 5.5 = -1.446221995
f = -1.446221995

Simplifying
f = -1.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {12.446221995, -1.446221995}

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