r^2-24r+37=0

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Solution for r^2-24r+37=0 equation:


Simplifying
r2 + -24r + 37 = 0

Reorder the terms:
37 + -24r + r2 = 0

Solving
37 + -24r + 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 + -24r + -37 + r2 = 0 + -37

Reorder the terms:
37 + -37 + -24r + r2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -24r + r2 = 0 + -37
-24r + r2 = 0 + -37

Combine like terms: 0 + -37 = -37
-24r + r2 = -37

The r term is -24r.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24r + 144 + r2 = -37 + 144

Reorder the terms:
144 + -24r + r2 = -37 + 144

Combine like terms: -37 + 144 = 107
144 + -24r + r2 = 107

Factor a perfect square on the left side:
(r + -12)(r + -12) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(r + -12) equal to 10.344080433 and -10.344080433.

Subproblem 1

r + -12 = 10.344080433 Simplifying r + -12 = 10.344080433 Reorder the terms: -12 + r = 10.344080433 Solving -12 + r = 10.344080433 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = 10.344080433 + 12 Combine like terms: -12 + 12 = 0 0 + r = 10.344080433 + 12 r = 10.344080433 + 12 Combine like terms: 10.344080433 + 12 = 22.344080433 r = 22.344080433 Simplifying r = 22.344080433

Subproblem 2

r + -12 = -10.344080433 Simplifying r + -12 = -10.344080433 Reorder the terms: -12 + r = -10.344080433 Solving -12 + r = -10.344080433 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = -10.344080433 + 12 Combine like terms: -12 + 12 = 0 0 + r = -10.344080433 + 12 r = -10.344080433 + 12 Combine like terms: -10.344080433 + 12 = 1.655919567 r = 1.655919567 Simplifying r = 1.655919567

Solution

The solution to the problem is based on the solutions from the subproblems. r = {22.344080433, 1.655919567}

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