.3f^2-3.5f+2=0

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Solution for .3f^2-3.5f+2=0 equation: 


Simplifying
0.3f2 + -3.5f + 2 = 0

Reorder the terms:
2 + -3.5f + 0.3f2 = 0

Solving
2 + -3.5f + 0.3f2 = 0

Solving for variable 'f'.

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

Divide each side by '0.3'.
6.666666667 + -11.66666667f + f2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -11.66666667f + -6.666666667 + f2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -11.66666667f + f2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -11.66666667f + f2 = 0 + -6.666666667
-11.66666667f + f2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-11.66666667f + f2 = -6.666666667

The f term is -11.66666667f.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667f + 34.02777780 + f2 = -6.666666667 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667f + f2 = -6.666666667 + 34.02777780

Combine like terms: -6.666666667 + 34.02777780 = 27.361111133
34.02777780 + -11.66666667f + f2 = 27.361111133

Factor a perfect square on the left side:
(f + -5.833333335)(f + -5.833333335) = 27.361111133

Calculate the square root of the right side: 5.230784944

Break this problem into two subproblems by setting 
(f + -5.833333335) equal to 5.230784944 and -5.230784944.


Subproblem 1
f + -5.833333335 = 5.230784944

Simplifying
f + -5.833333335 = 5.230784944

Reorder the terms:
-5.833333335 + f = 5.230784944

Solving
-5.833333335 + f = 5.230784944

Solving for variable 'f'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + f = 5.230784944 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + f = 5.230784944 + 5.833333335
f = 5.230784944 + 5.833333335

Combine like terms: 5.230784944 + 5.833333335 = 11.064118279
f = 11.064118279

Simplifying
f = 11.064118279


Subproblem 2
f + -5.833333335 = -5.230784944

Simplifying
f + -5.833333335 = -5.230784944

Reorder the terms:
-5.833333335 + f = -5.230784944

Solving
-5.833333335 + f = -5.230784944

Solving for variable 'f'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + f = -5.230784944 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + f = -5.230784944 + 5.833333335
f = -5.230784944 + 5.833333335

Combine like terms: -5.230784944 + 5.833333335 = 0.602548391
f = 0.602548391

Simplifying
f = 0.602548391


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {11.064118279, 0.602548391}

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