f^2+14f-9=0

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Solution for f^2+14f-9=0 equation:


Simplifying
f2 + 14f + -9 = 0

Reorder the terms:
-9 + 14f + f2 = 0

Solving
-9 + 14f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 14f + 9 + f2 = 0 + 9

Reorder the terms:
-9 + 9 + 14f + f2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 14f + f2 = 0 + 9
14f + f2 = 0 + 9

Combine like terms: 0 + 9 = 9
14f + f2 = 9

The f term is 14f.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14f + 49 + f2 = 9 + 49

Reorder the terms:
49 + 14f + f2 = 9 + 49

Combine like terms: 9 + 49 = 58
49 + 14f + f2 = 58

Factor a perfect square on the left side:
(f + 7)(f + 7) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(f + 7) equal to 7.615773106 and -7.615773106.


Subproblem 1
f + 7 = 7.615773106

Simplifying
f + 7 = 7.615773106

Reorder the terms:
7 + f = 7.615773106

Solving
7 + f = 7.615773106

Solving for variable 'f'.

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

Add '-7' to each side of the equation.
7 + -7 + f = 7.615773106 + -7

Combine like terms: 7 + -7 = 0
0 + f = 7.615773106 + -7
f = 7.615773106 + -7

Combine like terms: 7.615773106 + -7 = 0.615773106
f = 0.615773106

Simplifying
f = 0.615773106


Subproblem 2
f + 7 = -7.615773106

Simplifying
f + 7 = -7.615773106

Reorder the terms:
7 + f = -7.615773106

Solving
7 + f = -7.615773106

Solving for variable 'f'.

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

Add '-7' to each side of the equation.
7 + -7 + f = -7.615773106 + -7

Combine like terms: 7 + -7 = 0
0 + f = -7.615773106 + -7
f = -7.615773106 + -7

Combine like terms: -7.615773106 + -7 = -14.615773106
f = -14.615773106

Simplifying
f = -14.615773106


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.615773106, -14.615773106}

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