f^2+6f-17=0

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Solution for f^2+6f-17=0 equation:


Simplifying
f2 + 6f + -17 = 0

Reorder the terms:
-17 + 6f + f2 = 0

Solving
-17 + 6f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 6f + 17 + f2 = 0 + 17

Reorder the terms:
-17 + 17 + 6f + f2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 6f + f2 = 0 + 17
6f + f2 = 0 + 17

Combine like terms: 0 + 17 = 17
6f + f2 = 17

The f term is 6f.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6f + 9 + f2 = 17 + 9

Reorder the terms:
9 + 6f + f2 = 17 + 9

Combine like terms: 17 + 9 = 26
9 + 6f + f2 = 26

Factor a perfect square on the left side:
(f + 3)(f + 3) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(f + 3) equal to 5.099019514 and -5.099019514.

Subproblem 1

f + 3 = 5.099019514 Simplifying f + 3 = 5.099019514 Reorder the terms: 3 + f = 5.099019514 Solving 3 + f = 5.099019514 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + f = 5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + f = 5.099019514 + -3 f = 5.099019514 + -3 Combine like terms: 5.099019514 + -3 = 2.099019514 f = 2.099019514 Simplifying f = 2.099019514

Subproblem 2

f + 3 = -5.099019514 Simplifying f + 3 = -5.099019514 Reorder the terms: 3 + f = -5.099019514 Solving 3 + f = -5.099019514 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + f = -5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + f = -5.099019514 + -3 f = -5.099019514 + -3 Combine like terms: -5.099019514 + -3 = -8.099019514 f = -8.099019514 Simplifying f = -8.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. f = {2.099019514, -8.099019514}

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