r^2-6r-37=0

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Solution for r^2-6r-37=0 equation:


Simplifying
r2 + -6r + -37 = 0

Reorder the terms:
-37 + -6r + r2 = 0

Solving
-37 + -6r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -6r + 37 + r2 = 0 + 37

Reorder the terms:
-37 + 37 + -6r + r2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -6r + r2 = 0 + 37
-6r + r2 = 0 + 37

Combine like terms: 0 + 37 = 37
-6r + r2 = 37

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

Add '9' to each side of the equation.
-6r + 9 + r2 = 37 + 9

Reorder the terms:
9 + -6r + r2 = 37 + 9

Combine like terms: 37 + 9 = 46
9 + -6r + r2 = 46

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

Calculate the square root of the right side: 6.782329983

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

Subproblem 1

r + -3 = 6.782329983 Simplifying r + -3 = 6.782329983 Reorder the terms: -3 + r = 6.782329983 Solving -3 + r = 6.782329983 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + r = 6.782329983 + 3 r = 6.782329983 + 3 Combine like terms: 6.782329983 + 3 = 9.782329983 r = 9.782329983 Simplifying r = 9.782329983

Subproblem 2

r + -3 = -6.782329983 Simplifying r + -3 = -6.782329983 Reorder the terms: -3 + r = -6.782329983 Solving -3 + r = -6.782329983 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + r = -6.782329983 + 3 r = -6.782329983 + 3 Combine like terms: -6.782329983 + 3 = -3.782329983 r = -3.782329983 Simplifying r = -3.782329983

Solution

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

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