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Simplifying 17r + r2 = -53 Solving 17r + r2 = -53 Solving for variable 'r'. Reorder the terms: 53 + 17r + r2 = -53 + 53 Combine like terms: -53 + 53 = 0 53 + 17r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 17r + -53 + r2 = 0 + -53 Reorder the terms: 53 + -53 + 17r + r2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 17r + r2 = 0 + -53 17r + r2 = 0 + -53 Combine like terms: 0 + -53 = -53 17r + r2 = -53 The r term is 17r. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17r + 72.25 + r2 = -53 + 72.25 Reorder the terms: 72.25 + 17r + r2 = -53 + 72.25 Combine like terms: -53 + 72.25 = 19.25 72.25 + 17r + r2 = 19.25 Factor a perfect square on the left side: (r + 8.5)(r + 8.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (r + 8.5) equal to 4.387482194 and -4.387482194.Subproblem 1
r + 8.5 = 4.387482194 Simplifying r + 8.5 = 4.387482194 Reorder the terms: 8.5 + r = 4.387482194 Solving 8.5 + r = 4.387482194 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = 4.387482194 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = 4.387482194 + -8.5 r = 4.387482194 + -8.5 Combine like terms: 4.387482194 + -8.5 = -4.112517806 r = -4.112517806 Simplifying r = -4.112517806Subproblem 2
r + 8.5 = -4.387482194 Simplifying r + 8.5 = -4.387482194 Reorder the terms: 8.5 + r = -4.387482194 Solving 8.5 + r = -4.387482194 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = -4.387482194 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = -4.387482194 + -8.5 r = -4.387482194 + -8.5 Combine like terms: -4.387482194 + -8.5 = -12.887482194 r = -12.887482194 Simplifying r = -12.887482194Solution
The solution to the problem is based on the solutions from the subproblems. r = {-4.112517806, -12.887482194}
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