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Simplifying (r + -2)(r + 8) = 50 Reorder the terms: (-2 + r)(r + 8) = 50 Reorder the terms: (-2 + r)(8 + r) = 50 Multiply (-2 + r) * (8 + r) (-2(8 + r) + r(8 + r)) = 50 ((8 * -2 + r * -2) + r(8 + r)) = 50 ((-16 + -2r) + r(8 + r)) = 50 (-16 + -2r + (8 * r + r * r)) = 50 (-16 + -2r + (8r + r2)) = 50 Combine like terms: -2r + 8r = 6r (-16 + 6r + r2) = 50 Solving -16 + 6r + r2 = 50 Solving for variable 'r'. Reorder the terms: -16 + -50 + 6r + r2 = 50 + -50 Combine like terms: -16 + -50 = -66 -66 + 6r + r2 = 50 + -50 Combine like terms: 50 + -50 = 0 -66 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 6r + 66 + r2 = 0 + 66 Reorder the terms: -66 + 66 + 6r + r2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 6r + r2 = 0 + 66 6r + r2 = 0 + 66 Combine like terms: 0 + 66 = 66 6r + r2 = 66 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 66 + 9 Reorder the terms: 9 + 6r + r2 = 66 + 9 Combine like terms: 66 + 9 = 75 9 + 6r + r2 = 75 Factor a perfect square on the left side: (r + 3)(r + 3) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (r + 3) equal to 8.660254038 and -8.660254038.Subproblem 1
r + 3 = 8.660254038 Simplifying r + 3 = 8.660254038 Reorder the terms: 3 + r = 8.660254038 Solving 3 + r = 8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 8.660254038 + -3 Combine like terms: 3 + -3 = 0 0 + r = 8.660254038 + -3 r = 8.660254038 + -3 Combine like terms: 8.660254038 + -3 = 5.660254038 r = 5.660254038 Simplifying r = 5.660254038Subproblem 2
r + 3 = -8.660254038 Simplifying r + 3 = -8.660254038 Reorder the terms: 3 + r = -8.660254038 Solving 3 + r = -8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -8.660254038 + -3 Combine like terms: 3 + -3 = 0 0 + r = -8.660254038 + -3 r = -8.660254038 + -3 Combine like terms: -8.660254038 + -3 = -11.660254038 r = -11.660254038 Simplifying r = -11.660254038Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.660254038, -11.660254038}
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