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Simplifying (r + -2)(r + 18) = 25 Reorder the terms: (-2 + r)(r + 18) = 25 Reorder the terms: (-2 + r)(18 + r) = 25 Multiply (-2 + r) * (18 + r) (-2(18 + r) + r(18 + r)) = 25 ((18 * -2 + r * -2) + r(18 + r)) = 25 ((-36 + -2r) + r(18 + r)) = 25 (-36 + -2r + (18 * r + r * r)) = 25 (-36 + -2r + (18r + r2)) = 25 Combine like terms: -2r + 18r = 16r (-36 + 16r + r2) = 25 Solving -36 + 16r + r2 = 25 Solving for variable 'r'. Reorder the terms: -36 + -25 + 16r + r2 = 25 + -25 Combine like terms: -36 + -25 = -61 -61 + 16r + r2 = 25 + -25 Combine like terms: 25 + -25 = 0 -61 + 16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 16r + 61 + r2 = 0 + 61 Reorder the terms: -61 + 61 + 16r + r2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 16r + r2 = 0 + 61 16r + r2 = 0 + 61 Combine like terms: 0 + 61 = 61 16r + r2 = 61 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = 61 + 64 Reorder the terms: 64 + 16r + r2 = 61 + 64 Combine like terms: 61 + 64 = 125 64 + 16r + r2 = 125 Factor a perfect square on the left side: (r + 8)(r + 8) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (r + 8) equal to 11.180339887 and -11.180339887.Subproblem 1
r + 8 = 11.180339887 Simplifying r + 8 = 11.180339887 Reorder the terms: 8 + r = 11.180339887 Solving 8 + r = 11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + r = 11.180339887 + -8 r = 11.180339887 + -8 Combine like terms: 11.180339887 + -8 = 3.180339887 r = 3.180339887 Simplifying r = 3.180339887Subproblem 2
r + 8 = -11.180339887 Simplifying r + 8 = -11.180339887 Reorder the terms: 8 + r = -11.180339887 Solving 8 + r = -11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + r = -11.180339887 + -8 r = -11.180339887 + -8 Combine like terms: -11.180339887 + -8 = -19.180339887 r = -19.180339887 Simplifying r = -19.180339887Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.180339887, -19.180339887}
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