-2f^2-9f-2=0

Solution for -2f^2-9f-2=0 equation:

Simplifying
-2f2 + -9f + -2 = 0

Reorder the terms:
-2 + -9f + -2f2 = 0

Solving
-2 + -9f + -2f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 9f + 2f2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 9f + 2f2)' equal to zero and attempt to solve:

Simplifying
2 + 9f + 2f2 = 0

Solving
2 + 9f + 2f2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1 + 4.5f + f2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.5f + -1 + f2 = 0 + -1

Reorder the terms:
1 + -1 + 4.5f + f2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.5f + f2 = 0 + -1
4.5f + f2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.5f + f2 = -1

The f term is 4.5f.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5f + 5.0625 + f2 = -1 + 5.0625

Reorder the terms:
5.0625 + 4.5f + f2 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + 4.5f + f2 = 4.0625

Factor a perfect square on the left side:
(f + 2.25)(f + 2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(f + 2.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
f + 2.25 = 2.015564437

Simplifying
f + 2.25 = 2.015564437

Reorder the terms:
2.25 + f = 2.015564437

Solving
2.25 + f = 2.015564437

Solving for variable 'f'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + f = 2.015564437 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + f = 2.015564437 + -2.25
f = 2.015564437 + -2.25

Combine like terms: 2.015564437 + -2.25 = -0.234435563
f = -0.234435563

Simplifying
f = -0.234435563

Subproblem 2
f + 2.25 = -2.015564437

Simplifying
f + 2.25 = -2.015564437

Reorder the terms:
2.25 + f = -2.015564437

Solving
2.25 + f = -2.015564437

Solving for variable 'f'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + f = -2.015564437 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + f = -2.015564437 + -2.25
f = -2.015564437 + -2.25

Combine like terms: -2.015564437 + -2.25 = -4.265564437
f = -4.265564437

Simplifying
f = -4.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.234435563, -4.265564437}
Solution
f = {-0.234435563, -4.265564437}