f^2-9f+5=0

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Solution for f^2-9f+5=0 equation:


Simplifying
f2 + -9f + 5 = 0

Reorder the terms:
5 + -9f + f2 = 0

Solving
5 + -9f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -9f + -5 + f2 = 0 + -5

Reorder the terms:
5 + -5 + -9f + f2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9f + f2 = 0 + -5
-9f + f2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9f + f2 = -5

The f term is -9f.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9f + 20.25 + f2 = -5 + 20.25

Reorder the terms:
20.25 + -9f + f2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + -9f + f2 = 15.25

Factor a perfect square on the left side:
(f + -4.5)(f + -4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(f + -4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

f + -4.5 = 3.905124838 Simplifying f + -4.5 = 3.905124838 Reorder the terms: -4.5 + f = 3.905124838 Solving -4.5 + f = 3.905124838 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + f = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + f = 3.905124838 + 4.5 f = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 f = 8.405124838 Simplifying f = 8.405124838

Subproblem 2

f + -4.5 = -3.905124838 Simplifying f + -4.5 = -3.905124838 Reorder the terms: -4.5 + f = -3.905124838 Solving -4.5 + f = -3.905124838 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + f = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + f = -3.905124838 + 4.5 f = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 f = 0.594875162 Simplifying f = 0.594875162

Solution

The solution to the problem is based on the solutions from the subproblems. f = {8.405124838, 0.594875162}

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