2f^2+7f+2=0

Solution for 2f^2+7f+2=0 equation:

Simplifying
2f2 + 7f + 2 = 0

Reorder the terms:
2 + 7f + 2f2 = 0

Solving
2 + 7f + 2f2 = 0

Solving for variable 'f'.

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

Divide each side by '2'.
1 + 3.5f + f2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.5f + -1 + f2 = 0 + -1

Reorder the terms:
1 + -1 + 3.5f + f2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.5f + f2 = 0 + -1
3.5f + f2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.5f + f2 = -1

The f term is 3.5f.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5f + 3.0625 + f2 = -1 + 3.0625

Reorder the terms:
3.0625 + 3.5f + f2 = -1 + 3.0625

Combine like terms: -1 + 3.0625 = 2.0625
3.0625 + 3.5f + f2 = 2.0625

Factor a perfect square on the left side:
(f + 1.75)(f + 1.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(f + 1.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
f + 1.75 = 1.436140662

Simplifying
f + 1.75 = 1.436140662

Reorder the terms:
1.75 + f = 1.436140662

Solving
1.75 + f = 1.436140662

Solving for variable 'f'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + f = 1.436140662 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + f = 1.436140662 + -1.75
f = 1.436140662 + -1.75

Combine like terms: 1.436140662 + -1.75 = -0.313859338
f = -0.313859338

Simplifying
f = -0.313859338

Subproblem 2
f + 1.75 = -1.436140662

Simplifying
f + 1.75 = -1.436140662

Reorder the terms:
1.75 + f = -1.436140662

Solving
1.75 + f = -1.436140662

Solving for variable 'f'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + f = -1.436140662 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + f = -1.436140662 + -1.75
f = -1.436140662 + -1.75

Combine like terms: -1.436140662 + -1.75 = -3.186140662
f = -3.186140662

Simplifying
f = -3.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.313859338, -3.186140662}