f^2+6f=37

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Solution for f^2+6f=37 equation:


Simplifying
f2 + 6f = 37

Reorder the terms:
6f + f2 = 37

Solving
6f + f2 = 37

Solving for variable 'f'.

Reorder the terms:
-37 + 6f + f2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 6f + f2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 6f + 37 + f2 = 0 + 37

Reorder the terms:
-37 + 37 + 6f + f2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 6f + f2 = 0 + 37
6f + f2 = 0 + 37

Combine like terms: 0 + 37 = 37
6f + f2 = 37

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 = 37 + 9

Reorder the terms:
9 + 6f + f2 = 37 + 9

Combine like terms: 37 + 9 = 46
9 + 6f + f2 = 46

Factor a perfect square on the left side:
(f + 3)(f + 3) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(f + 3) equal to 6.782329983 and -6.782329983.

Subproblem 1

f + 3 = 6.782329983 Simplifying f + 3 = 6.782329983 Reorder the terms: 3 + f = 6.782329983 Solving 3 + f = 6.782329983 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 = 6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + f = 6.782329983 + -3 f = 6.782329983 + -3 Combine like terms: 6.782329983 + -3 = 3.782329983 f = 3.782329983 Simplifying f = 3.782329983

Subproblem 2

f + 3 = -6.782329983 Simplifying f + 3 = -6.782329983 Reorder the terms: 3 + f = -6.782329983 Solving 3 + f = -6.782329983 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 = -6.782329983 + -3 Combine like terms: 3 + -3 = 0 0 + f = -6.782329983 + -3 f = -6.782329983 + -3 Combine like terms: -6.782329983 + -3 = -9.782329983 f = -9.782329983 Simplifying f = -9.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. f = {3.782329983, -9.782329983}

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