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Simplifying (r + -2)(r + 8) = 20 Reorder the terms: (-2 + r)(r + 8) = 20 Reorder the terms: (-2 + r)(8 + r) = 20 Multiply (-2 + r) * (8 + r) (-2(8 + r) + r(8 + r)) = 20 ((8 * -2 + r * -2) + r(8 + r)) = 20 ((-16 + -2r) + r(8 + r)) = 20 (-16 + -2r + (8 * r + r * r)) = 20 (-16 + -2r + (8r + r2)) = 20 Combine like terms: -2r + 8r = 6r (-16 + 6r + r2) = 20 Solving -16 + 6r + r2 = 20 Solving for variable 'r'. Reorder the terms: -16 + -20 + 6r + r2 = 20 + -20 Combine like terms: -16 + -20 = -36 -36 + 6r + r2 = 20 + -20 Combine like terms: 20 + -20 = 0 -36 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6r + 36 + r2 = 0 + 36 Reorder the terms: -36 + 36 + 6r + r2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6r + r2 = 0 + 36 6r + r2 = 0 + 36 Combine like terms: 0 + 36 = 36 6r + r2 = 36 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 = 36 + 9 Reorder the terms: 9 + 6r + r2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6r + r2 = 45 Factor a perfect square on the left side: (r + 3)(r + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
r + 3 = 6.708203933 Simplifying r + 3 = 6.708203933 Reorder the terms: 3 + r = 6.708203933 Solving 3 + r = 6.708203933 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 = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + r = 6.708203933 + -3 r = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 r = 3.708203933 Simplifying r = 3.708203933Subproblem 2
r + 3 = -6.708203933 Simplifying r + 3 = -6.708203933 Reorder the terms: 3 + r = -6.708203933 Solving 3 + r = -6.708203933 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 = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + r = -6.708203933 + -3 r = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 r = -9.708203933 Simplifying r = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.708203933, -9.708203933}
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