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Simplifying (r + -2)(r + 8) = 100 Reorder the terms: (-2 + r)(r + 8) = 100 Reorder the terms: (-2 + r)(8 + r) = 100 Multiply (-2 + r) * (8 + r) (-2(8 + r) + r(8 + r)) = 100 ((8 * -2 + r * -2) + r(8 + r)) = 100 ((-16 + -2r) + r(8 + r)) = 100 (-16 + -2r + (8 * r + r * r)) = 100 (-16 + -2r + (8r + r2)) = 100 Combine like terms: -2r + 8r = 6r (-16 + 6r + r2) = 100 Solving -16 + 6r + r2 = 100 Solving for variable 'r'. Reorder the terms: -16 + -100 + 6r + r2 = 100 + -100 Combine like terms: -16 + -100 = -116 -116 + 6r + r2 = 100 + -100 Combine like terms: 100 + -100 = 0 -116 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 6r + 116 + r2 = 0 + 116 Reorder the terms: -116 + 116 + 6r + r2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 6r + r2 = 0 + 116 6r + r2 = 0 + 116 Combine like terms: 0 + 116 = 116 6r + r2 = 116 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 = 116 + 9 Reorder the terms: 9 + 6r + r2 = 116 + 9 Combine like terms: 116 + 9 = 125 9 + 6r + r2 = 125 Factor a perfect square on the left side: (r + 3)(r + 3) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (r + 3) equal to 11.180339887 and -11.180339887.Subproblem 1
r + 3 = 11.180339887 Simplifying r + 3 = 11.180339887 Reorder the terms: 3 + r = 11.180339887 Solving 3 + r = 11.180339887 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 = 11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + r = 11.180339887 + -3 r = 11.180339887 + -3 Combine like terms: 11.180339887 + -3 = 8.180339887 r = 8.180339887 Simplifying r = 8.180339887Subproblem 2
r + 3 = -11.180339887 Simplifying r + 3 = -11.180339887 Reorder the terms: 3 + r = -11.180339887 Solving 3 + r = -11.180339887 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 = -11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + r = -11.180339887 + -3 r = -11.180339887 + -3 Combine like terms: -11.180339887 + -3 = -14.180339887 r = -14.180339887 Simplifying r = -14.180339887Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.180339887, -14.180339887}
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