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Simplifying r2 + -24r = 5 Reorder the terms: -24r + r2 = 5 Solving -24r + r2 = 5 Solving for variable 'r'. Reorder the terms: -5 + -24r + r2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -24r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -24r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + -24r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -24r + r2 = 0 + 5 -24r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 -24r + r2 = 5 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 = 5 + 144 Reorder the terms: 144 + -24r + r2 = 5 + 144 Combine like terms: 5 + 144 = 149 144 + -24r + r2 = 149 Factor a perfect square on the left side: (r + -12)(r + -12) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (r + -12) equal to 12.206555616 and -12.206555616.Subproblem 1
r + -12 = 12.206555616 Simplifying r + -12 = 12.206555616 Reorder the terms: -12 + r = 12.206555616 Solving -12 + r = 12.206555616 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 = 12.206555616 + 12 Combine like terms: -12 + 12 = 0 0 + r = 12.206555616 + 12 r = 12.206555616 + 12 Combine like terms: 12.206555616 + 12 = 24.206555616 r = 24.206555616 Simplifying r = 24.206555616Subproblem 2
r + -12 = -12.206555616 Simplifying r + -12 = -12.206555616 Reorder the terms: -12 + r = -12.206555616 Solving -12 + r = -12.206555616 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 = -12.206555616 + 12 Combine like terms: -12 + 12 = 0 0 + r = -12.206555616 + 12 r = -12.206555616 + 12 Combine like terms: -12.206555616 + 12 = -0.206555616 r = -0.206555616 Simplifying r = -0.206555616Solution
The solution to the problem is based on the solutions from the subproblems. r = {24.206555616, -0.206555616}
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