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Simplifying r2 + 5r + -60 = 0 Reorder the terms: -60 + 5r + r2 = 0 Solving -60 + 5r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 5r + 60 + r2 = 0 + 60 Reorder the terms: -60 + 60 + 5r + r2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 5r + r2 = 0 + 60 5r + r2 = 0 + 60 Combine like terms: 0 + 60 = 60 5r + r2 = 60 The r term is 5r. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5r + 6.25 + r2 = 60 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 60 + 6.25 Combine like terms: 60 + 6.25 = 66.25 6.25 + 5r + r2 = 66.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (r + 2.5) equal to 8.139410298 and -8.139410298.Subproblem 1
r + 2.5 = 8.139410298 Simplifying r + 2.5 = 8.139410298 Reorder the terms: 2.5 + r = 8.139410298 Solving 2.5 + r = 8.139410298 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 8.139410298 + -2.5 r = 8.139410298 + -2.5 Combine like terms: 8.139410298 + -2.5 = 5.639410298 r = 5.639410298 Simplifying r = 5.639410298Subproblem 2
r + 2.5 = -8.139410298 Simplifying r + 2.5 = -8.139410298 Reorder the terms: 2.5 + r = -8.139410298 Solving 2.5 + r = -8.139410298 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -8.139410298 + -2.5 r = -8.139410298 + -2.5 Combine like terms: -8.139410298 + -2.5 = -10.639410298 r = -10.639410298 Simplifying r = -10.639410298Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.639410298, -10.639410298}
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