f^2+3f-47=0

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Solution for f^2+3f-47=0 equation:


Simplifying
f2 + 3f + -47 = 0

Reorder the terms:
-47 + 3f + f2 = 0

Solving
-47 + 3f + f2 = 0

Solving for variable 'f'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 3f + 47 + f2 = 0 + 47

Reorder the terms:
-47 + 47 + 3f + f2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 3f + f2 = 0 + 47
3f + f2 = 0 + 47

Combine like terms: 0 + 47 = 47
3f + f2 = 47

The f term is 3f.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3f + 2.25 + f2 = 47 + 2.25

Reorder the terms:
2.25 + 3f + f2 = 47 + 2.25

Combine like terms: 47 + 2.25 = 49.25
2.25 + 3f + f2 = 49.25

Factor a perfect square on the left side:
(f + 1.5)(f + 1.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(f + 1.5) equal to 7.017834424 and -7.017834424.

Subproblem 1

f + 1.5 = 7.017834424 Simplifying f + 1.5 = 7.017834424 Reorder the terms: 1.5 + f = 7.017834424 Solving 1.5 + f = 7.017834424 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + f = 7.017834424 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + f = 7.017834424 + -1.5 f = 7.017834424 + -1.5 Combine like terms: 7.017834424 + -1.5 = 5.517834424 f = 5.517834424 Simplifying f = 5.517834424

Subproblem 2

f + 1.5 = -7.017834424 Simplifying f + 1.5 = -7.017834424 Reorder the terms: 1.5 + f = -7.017834424 Solving 1.5 + f = -7.017834424 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + f = -7.017834424 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + f = -7.017834424 + -1.5 f = -7.017834424 + -1.5 Combine like terms: -7.017834424 + -1.5 = -8.517834424 f = -8.517834424 Simplifying f = -8.517834424

Solution

The solution to the problem is based on the solutions from the subproblems. f = {5.517834424, -8.517834424}

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