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Simplifying r2 + 18r = -43 Reorder the terms: 18r + r2 = -43 Solving 18r + r2 = -43 Solving for variable 'r'. Reorder the terms: 43 + 18r + r2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 18r + -43 + r2 = 0 + -43 Reorder the terms: 43 + -43 + 18r + r2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 18r + r2 = 0 + -43 18r + r2 = 0 + -43 Combine like terms: 0 + -43 = -43 18r + r2 = -43 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 = -43 + 81 Reorder the terms: 81 + 18r + r2 = -43 + 81 Combine like terms: -43 + 81 = 38 81 + 18r + r2 = 38 Factor a perfect square on the left side: (r + 9)(r + 9) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (r + 9) equal to 6.164414003 and -6.164414003.Subproblem 1
r + 9 = 6.164414003 Simplifying r + 9 = 6.164414003 Reorder the terms: 9 + r = 6.164414003 Solving 9 + r = 6.164414003 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 = 6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + r = 6.164414003 + -9 r = 6.164414003 + -9 Combine like terms: 6.164414003 + -9 = -2.835585997 r = -2.835585997 Simplifying r = -2.835585997Subproblem 2
r + 9 = -6.164414003 Simplifying r + 9 = -6.164414003 Reorder the terms: 9 + r = -6.164414003 Solving 9 + r = -6.164414003 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 = -6.164414003 + -9 Combine like terms: 9 + -9 = 0 0 + r = -6.164414003 + -9 r = -6.164414003 + -9 Combine like terms: -6.164414003 + -9 = -15.164414003 r = -15.164414003 Simplifying r = -15.164414003Solution
The solution to the problem is based on the solutions from the subproblems. r = {-2.835585997, -15.164414003}
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