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Simplifying (r + -2)(r + 10) = 9 Reorder the terms: (-2 + r)(r + 10) = 9 Reorder the terms: (-2 + r)(10 + r) = 9 Multiply (-2 + r) * (10 + r) (-2(10 + r) + r(10 + r)) = 9 ((10 * -2 + r * -2) + r(10 + r)) = 9 ((-20 + -2r) + r(10 + r)) = 9 (-20 + -2r + (10 * r + r * r)) = 9 (-20 + -2r + (10r + r2)) = 9 Combine like terms: -2r + 10r = 8r (-20 + 8r + r2) = 9 Solving -20 + 8r + r2 = 9 Solving for variable 'r'. Reorder the terms: -20 + -9 + 8r + r2 = 9 + -9 Combine like terms: -20 + -9 = -29 -29 + 8r + r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -29 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 8r + 29 + r2 = 0 + 29 Reorder the terms: -29 + 29 + 8r + r2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 8r + r2 = 0 + 29 8r + r2 = 0 + 29 Combine like terms: 0 + 29 = 29 8r + r2 = 29 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 = 29 + 16 Reorder the terms: 16 + 8r + r2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + 8r + r2 = 45 Factor a perfect square on the left side: (r + 4)(r + 4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + 4) equal to 6.708203933 and -6.708203933.Subproblem 1
r + 4 = 6.708203933 Simplifying r + 4 = 6.708203933 Reorder the terms: 4 + r = 6.708203933 Solving 4 + r = 6.708203933 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 = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.708203933 + -4 r = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 r = 2.708203933 Simplifying r = 2.708203933Subproblem 2
r + 4 = -6.708203933 Simplifying r + 4 = -6.708203933 Reorder the terms: 4 + r = -6.708203933 Solving 4 + r = -6.708203933 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 = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.708203933 + -4 r = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 r = -10.708203933 Simplifying r = -10.708203933Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.708203933, -10.708203933}
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