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