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Simplifying (r + 5)(r + 3) = 18 Reorder the terms: (5 + r)(r + 3) = 18 Reorder the terms: (5 + r)(3 + r) = 18 Multiply (5 + r) * (3 + r) (5(3 + r) + r(3 + r)) = 18 ((3 * 5 + r * 5) + r(3 + r)) = 18 ((15 + 5r) + r(3 + r)) = 18 (15 + 5r + (3 * r + r * r)) = 18 (15 + 5r + (3r + r2)) = 18 Combine like terms: 5r + 3r = 8r (15 + 8r + r2) = 18 Solving 15 + 8r + r2 = 18 Solving for variable 'r'. Reorder the terms: 15 + -18 + 8r + r2 = 18 + -18 Combine like terms: 15 + -18 = -3 -3 + 8r + r2 = 18 + -18 Combine like terms: 18 + -18 = 0 -3 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + 8r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8r + r2 = 0 + 3 8r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 8r + r2 = 3 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 3 + 16 Reorder the terms: 16 + 8r + r2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8r + r2 = 19 Factor a perfect square on the left side: (r + 4)(r + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (r + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
r + 4 = 4.358898944 Simplifying r + 4 = 4.358898944 Reorder the terms: 4 + r = 4.358898944 Solving 4 + r = 4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + r = 4.358898944 + -4 r = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 r = 0.358898944 Simplifying r = 0.358898944Subproblem 2
r + 4 = -4.358898944 Simplifying r + 4 = -4.358898944 Reorder the terms: 4 + r = -4.358898944 Solving 4 + r = -4.358898944 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + r = -4.358898944 + -4 r = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 r = -8.358898944 Simplifying r = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.358898944, -8.358898944}
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