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Simplifying r2 + 15r + -91.5 = 0 Reorder the terms: -91.5 + 15r + r2 = 0 Solving -91.5 + 15r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '91.5' to each side of the equation. -91.5 + 15r + 91.5 + r2 = 0 + 91.5 Reorder the terms: -91.5 + 91.5 + 15r + r2 = 0 + 91.5 Combine like terms: -91.5 + 91.5 = 0.0 0.0 + 15r + r2 = 0 + 91.5 15r + r2 = 0 + 91.5 Combine like terms: 0 + 91.5 = 91.5 15r + r2 = 91.5 The r term is 15r. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15r + 56.25 + r2 = 91.5 + 56.25 Reorder the terms: 56.25 + 15r + r2 = 91.5 + 56.25 Combine like terms: 91.5 + 56.25 = 147.75 56.25 + 15r + r2 = 147.75 Factor a perfect square on the left side: (r + 7.5)(r + 7.5) = 147.75 Calculate the square root of the right side: 12.155245781 Break this problem into two subproblems by setting (r + 7.5) equal to 12.155245781 and -12.155245781.Subproblem 1
r + 7.5 = 12.155245781 Simplifying r + 7.5 = 12.155245781 Reorder the terms: 7.5 + r = 12.155245781 Solving 7.5 + r = 12.155245781 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = 12.155245781 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 12.155245781 + -7.5 r = 12.155245781 + -7.5 Combine like terms: 12.155245781 + -7.5 = 4.655245781 r = 4.655245781 Simplifying r = 4.655245781Subproblem 2
r + 7.5 = -12.155245781 Simplifying r + 7.5 = -12.155245781 Reorder the terms: 7.5 + r = -12.155245781 Solving 7.5 + r = -12.155245781 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = -12.155245781 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -12.155245781 + -7.5 r = -12.155245781 + -7.5 Combine like terms: -12.155245781 + -7.5 = -19.655245781 r = -19.655245781 Simplifying r = -19.655245781Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.655245781, -19.655245781}
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