4f-2f^2=100

Solution for 4f-2f^2=100 equation:

Simplifying
4f + -2f2 = 100

Solving
4f + -2f2 = 100

Solving for variable 'f'.

Reorder the terms:
-100 + 4f + -2f2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 4f + -2f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 2f + -1f2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 2f + -1f2)' equal to zero and attempt to solve:

Simplifying
-50 + 2f + -1f2 = 0

Solving
-50 + 2f + -1f2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
50 + -2f + f2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -2f + -50 + f2 = 0 + -50

Reorder the terms:
50 + -50 + -2f + f2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -2f + f2 = 0 + -50
-2f + f2 = 0 + -50

Combine like terms: 0 + -50 = -50
-2f + f2 = -50

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 = -50 + 1

Reorder the terms:
1 + -2f + f2 = -50 + 1

Combine like terms: -50 + 1 = -49
1 + -2f + f2 = -49

Factor a perfect square on the left side:
(f + -1)(f + -1) = -49

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.