f^2-18f=25

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Solution for f^2-18f=25 equation: 


Simplifying
f2 + -18f = 25

Reorder the terms:
-18f + f2 = 25

Solving
-18f + f2 = 25

Solving for variable 'f'.

Reorder the terms:
-25 + -18f + f2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -18f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -18f + 25 + f2 = 0 + 25

Reorder the terms:
-25 + 25 + -18f + f2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -18f + f2 = 0 + 25
-18f + f2 = 0 + 25

Combine like terms: 0 + 25 = 25
-18f + f2 = 25

The f term is -18f.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18f + 81 + f2 = 25 + 81

Reorder the terms:
81 + -18f + f2 = 25 + 81

Combine like terms: 25 + 81 = 106
81 + -18f + f2 = 106

Factor a perfect square on the left side:
(f + -9)(f + -9) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(f + -9) equal to 10.295630141 and -10.295630141.


Subproblem 1
f + -9 = 10.295630141

Simplifying
f + -9 = 10.295630141

Reorder the terms:
-9 + f = 10.295630141

Solving
-9 + f = 10.295630141

Solving for variable 'f'.

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

Add '9' to each side of the equation.
-9 + 9 + f = 10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + f = 10.295630141 + 9
f = 10.295630141 + 9

Combine like terms: 10.295630141 + 9 = 19.295630141
f = 19.295630141

Simplifying
f = 19.295630141


Subproblem 2
f + -9 = -10.295630141

Simplifying
f + -9 = -10.295630141

Reorder the terms:
-9 + f = -10.295630141

Solving
-9 + f = -10.295630141

Solving for variable 'f'.

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

Add '9' to each side of the equation.
-9 + 9 + f = -10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + f = -10.295630141 + 9
f = -10.295630141 + 9

Combine like terms: -10.295630141 + 9 = -1.295630141
f = -1.295630141

Simplifying
f = -1.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {19.295630141, -1.295630141}

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