-4f^2+80f-188=0

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Solution for -4f^2+80f-188=0 equation: 


Simplifying
-4f2 + 80f + -188 = 0

Reorder the terms:
-188 + 80f + -4f2 = 0

Solving
-188 + 80f + -4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-47 + 20f + -1f2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-47 + 20f + -1f2)' equal to zero and attempt to solve:

Simplifying
-47 + 20f + -1f2 = 0

Solving
-47 + 20f + -1f2 = 0

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

Divide each side by '-1'.
47 + -20f + f2 = 0

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + -20f + -47 + f2 = 0 + -47

Reorder the terms:
47 + -47 + -20f + f2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -20f + f2 = 0 + -47
-20f + f2 = 0 + -47

Combine like terms: 0 + -47 = -47
-20f + f2 = -47

The f term is -20f.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20f + 100 + f2 = -47 + 100

Reorder the terms:
100 + -20f + f2 = -47 + 100

Combine like terms: -47 + 100 = 53
100 + -20f + f2 = 53

Factor a perfect square on the left side:
(f + -10)(f + -10) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(f + -10) equal to 7.280109889 and -7.280109889.


Subproblem 1
f + -10 = 7.280109889

Simplifying
f + -10 = 7.280109889

Reorder the terms:
-10 + f = 7.280109889

Solving
-10 + f = 7.280109889

Solving for variable 'f'.

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

Add '10' to each side of the equation.
-10 + 10 + f = 7.280109889 + 10

Combine like terms: -10 + 10 = 0
0 + f = 7.280109889 + 10
f = 7.280109889 + 10

Combine like terms: 7.280109889 + 10 = 17.280109889
f = 17.280109889

Simplifying
f = 17.280109889


Subproblem 2
f + -10 = -7.280109889

Simplifying
f + -10 = -7.280109889

Reorder the terms:
-10 + f = -7.280109889

Solving
-10 + f = -7.280109889

Solving for variable 'f'.

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

Add '10' to each side of the equation.
-10 + 10 + f = -7.280109889 + 10

Combine like terms: -10 + 10 = 0
0 + f = -7.280109889 + 10
f = -7.280109889 + 10

Combine like terms: -7.280109889 + 10 = 2.719890111
f = 2.719890111

Simplifying
f = 2.719890111


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {17.280109889, 2.719890111}
Solution
f = {17.280109889, 2.719890111}

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