f^2-2f-29=0

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Solution for f^2-2f-29=0 equation:


Simplifying
f2 + -2f + -29 = 0

Reorder the terms:
-29 + -2f + f2 = 0

Solving
-29 + -2f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -2f + 29 + f2 = 0 + 29

Reorder the terms:
-29 + 29 + -2f + f2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -2f + f2 = 0 + 29
-2f + f2 = 0 + 29

Combine like terms: 0 + 29 = 29
-2f + f2 = 29

The f term is -2f.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2f + 1 + f2 = 29 + 1

Reorder the terms:
1 + -2f + f2 = 29 + 1

Combine like terms: 29 + 1 = 30
1 + -2f + f2 = 30

Factor a perfect square on the left side:
(f + -1)(f + -1) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(f + -1) equal to 5.477225575 and -5.477225575.

Subproblem 1

f + -1 = 5.477225575 Simplifying f + -1 = 5.477225575 Reorder the terms: -1 + f = 5.477225575 Solving -1 + f = 5.477225575 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + f = 5.477225575 + 1 Combine like terms: -1 + 1 = 0 0 + f = 5.477225575 + 1 f = 5.477225575 + 1 Combine like terms: 5.477225575 + 1 = 6.477225575 f = 6.477225575 Simplifying f = 6.477225575

Subproblem 2

f + -1 = -5.477225575 Simplifying f + -1 = -5.477225575 Reorder the terms: -1 + f = -5.477225575 Solving -1 + f = -5.477225575 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + f = -5.477225575 + 1 Combine like terms: -1 + 1 = 0 0 + f = -5.477225575 + 1 f = -5.477225575 + 1 Combine like terms: -5.477225575 + 1 = -4.477225575 f = -4.477225575 Simplifying f = -4.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. f = {6.477225575, -4.477225575}

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