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Simplifying (R + 2)(R + 6) = 15 Reorder the terms: (2 + R)(R + 6) = 15 Reorder the terms: (2 + R)(6 + R) = 15 Multiply (2 + R) * (6 + R) (2(6 + R) + R(6 + R)) = 15 ((6 * 2 + R * 2) + R(6 + R)) = 15 ((12 + 2R) + R(6 + R)) = 15 (12 + 2R + (6 * R + R * R)) = 15 (12 + 2R + (6R + R2)) = 15 Combine like terms: 2R + 6R = 8R (12 + 8R + R2) = 15 Solving 12 + 8R + R2 = 15 Solving for variable 'R'. Reorder the terms: 12 + -15 + 8R + R2 = 15 + -15 Combine like terms: 12 + -15 = -3 -3 + 8R + R2 = 15 + -15 Combine like terms: 15 + -15 = 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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