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Simplifying 2r2 + 36r + -373 = 0 Reorder the terms: -373 + 36r + 2r2 = 0 Solving -373 + 36r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -186.5 + 18r + r2 = 0 Move the constant term to the right: Add '186.5' to each side of the equation. -186.5 + 18r + 186.5 + r2 = 0 + 186.5 Reorder the terms: -186.5 + 186.5 + 18r + r2 = 0 + 186.5 Combine like terms: -186.5 + 186.5 = 0.0 0.0 + 18r + r2 = 0 + 186.5 18r + r2 = 0 + 186.5 Combine like terms: 0 + 186.5 = 186.5 18r + r2 = 186.5 The r term is 18r. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18r + 81 + r2 = 186.5 + 81 Reorder the terms: 81 + 18r + r2 = 186.5 + 81 Combine like terms: 186.5 + 81 = 267.5 81 + 18r + r2 = 267.5 Factor a perfect square on the left side: (r + 9)(r + 9) = 267.5 Calculate the square root of the right side: 16.355427234 Break this problem into two subproblems by setting (r + 9) equal to 16.355427234 and -16.355427234.Subproblem 1
r + 9 = 16.355427234 Simplifying r + 9 = 16.355427234 Reorder the terms: 9 + r = 16.355427234 Solving 9 + r = 16.355427234 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = 16.355427234 + -9 Combine like terms: 9 + -9 = 0 0 + r = 16.355427234 + -9 r = 16.355427234 + -9 Combine like terms: 16.355427234 + -9 = 7.355427234 r = 7.355427234 Simplifying r = 7.355427234Subproblem 2
r + 9 = -16.355427234 Simplifying r + 9 = -16.355427234 Reorder the terms: 9 + r = -16.355427234 Solving 9 + r = -16.355427234 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = -16.355427234 + -9 Combine like terms: 9 + -9 = 0 0 + r = -16.355427234 + -9 r = -16.355427234 + -9 Combine like terms: -16.355427234 + -9 = -25.355427234 r = -25.355427234 Simplifying r = -25.355427234Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.355427234, -25.355427234}
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