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Simplifying r2 + 18r + 16 = 45 Reorder the terms: 16 + 18r + r2 = 45 Solving 16 + 18r + r2 = 45 Solving for variable 'r'. Reorder the terms: 16 + -45 + 18r + r2 = 45 + -45 Combine like terms: 16 + -45 = -29 -29 + 18r + r2 = 45 + -45 Combine like terms: 45 + -45 = 0 -29 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 18r + 29 + r2 = 0 + 29 Reorder the terms: -29 + 29 + 18r + r2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 18r + r2 = 0 + 29 18r + r2 = 0 + 29 Combine like terms: 0 + 29 = 29 18r + r2 = 29 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 = 29 + 81 Reorder the terms: 81 + 18r + r2 = 29 + 81 Combine like terms: 29 + 81 = 110 81 + 18r + r2 = 110 Factor a perfect square on the left side: (r + 9)(r + 9) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (r + 9) equal to 10.488088482 and -10.488088482.Subproblem 1
r + 9 = 10.488088482 Simplifying r + 9 = 10.488088482 Reorder the terms: 9 + r = 10.488088482 Solving 9 + r = 10.488088482 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 = 10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + r = 10.488088482 + -9 r = 10.488088482 + -9 Combine like terms: 10.488088482 + -9 = 1.488088482 r = 1.488088482 Simplifying r = 1.488088482Subproblem 2
r + 9 = -10.488088482 Simplifying r + 9 = -10.488088482 Reorder the terms: 9 + r = -10.488088482 Solving 9 + r = -10.488088482 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 = -10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + r = -10.488088482 + -9 r = -10.488088482 + -9 Combine like terms: -10.488088482 + -9 = -19.488088482 r = -19.488088482 Simplifying r = -19.488088482Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.488088482, -19.488088482}
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