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Simplifying r2 + -24r + 64 = 0 Reorder the terms: 64 + -24r + r2 = 0 Solving 64 + -24r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -24r + -64 + r2 = 0 + -64 Reorder the terms: 64 + -64 + -24r + r2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -24r + r2 = 0 + -64 -24r + r2 = 0 + -64 Combine like terms: 0 + -64 = -64 -24r + r2 = -64 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 = -64 + 144 Reorder the terms: 144 + -24r + r2 = -64 + 144 Combine like terms: -64 + 144 = 80 144 + -24r + r2 = 80 Factor a perfect square on the left side: (r + -12)(r + -12) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (r + -12) equal to 8.94427191 and -8.94427191.Subproblem 1
r + -12 = 8.94427191 Simplifying r + -12 = 8.94427191 Reorder the terms: -12 + r = 8.94427191 Solving -12 + r = 8.94427191 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 = 8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + r = 8.94427191 + 12 r = 8.94427191 + 12 Combine like terms: 8.94427191 + 12 = 20.94427191 r = 20.94427191 Simplifying r = 20.94427191Subproblem 2
r + -12 = -8.94427191 Simplifying r + -12 = -8.94427191 Reorder the terms: -12 + r = -8.94427191 Solving -12 + r = -8.94427191 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 = -8.94427191 + 12 Combine like terms: -12 + 12 = 0 0 + r = -8.94427191 + 12 r = -8.94427191 + 12 Combine like terms: -8.94427191 + 12 = 3.05572809 r = 3.05572809 Simplifying r = 3.05572809Solution
The solution to the problem is based on the solutions from the subproblems. r = {20.94427191, 3.05572809}
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