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Simplifying r2 + 15r + -500 = 0 Reorder the terms: -500 + 15r + r2 = 0 Solving -500 + 15r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 15r + 500 + r2 = 0 + 500 Reorder the terms: -500 + 500 + 15r + r2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 15r + r2 = 0 + 500 15r + r2 = 0 + 500 Combine like terms: 0 + 500 = 500 15r + r2 = 500 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 = 500 + 56.25 Reorder the terms: 56.25 + 15r + r2 = 500 + 56.25 Combine like terms: 500 + 56.25 = 556.25 56.25 + 15r + r2 = 556.25 Factor a perfect square on the left side: (r + 7.5)(r + 7.5) = 556.25 Calculate the square root of the right side: 23.58495283 Break this problem into two subproblems by setting (r + 7.5) equal to 23.58495283 and -23.58495283.Subproblem 1
r + 7.5 = 23.58495283 Simplifying r + 7.5 = 23.58495283 Reorder the terms: 7.5 + r = 23.58495283 Solving 7.5 + r = 23.58495283 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 = 23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 23.58495283 + -7.5 r = 23.58495283 + -7.5 Combine like terms: 23.58495283 + -7.5 = 16.08495283 r = 16.08495283 Simplifying r = 16.08495283Subproblem 2
r + 7.5 = -23.58495283 Simplifying r + 7.5 = -23.58495283 Reorder the terms: 7.5 + r = -23.58495283 Solving 7.5 + r = -23.58495283 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 = -23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -23.58495283 + -7.5 r = -23.58495283 + -7.5 Combine like terms: -23.58495283 + -7.5 = -31.08495283 r = -31.08495283 Simplifying r = -31.08495283Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.08495283, -31.08495283}
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