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Simplifying (r + -4)(r + 8) = -9 Reorder the terms: (-4 + r)(r + 8) = -9 Reorder the terms: (-4 + r)(8 + r) = -9 Multiply (-4 + r) * (8 + r) (-4(8 + r) + r(8 + r)) = -9 ((8 * -4 + r * -4) + r(8 + r)) = -9 ((-32 + -4r) + r(8 + r)) = -9 (-32 + -4r + (8 * r + r * r)) = -9 (-32 + -4r + (8r + r2)) = -9 Combine like terms: -4r + 8r = 4r (-32 + 4r + r2) = -9 Solving -32 + 4r + r2 = -9 Solving for variable 'r'. Reorder the terms: -32 + 9 + 4r + r2 = -9 + 9 Combine like terms: -32 + 9 = -23 -23 + 4r + r2 = -9 + 9 Combine like terms: -9 + 9 = 0 -23 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 4r + 23 + r2 = 0 + 23 Reorder the terms: -23 + 23 + 4r + r2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 4r + r2 = 0 + 23 4r + r2 = 0 + 23 Combine like terms: 0 + 23 = 23 4r + r2 = 23 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 23 + 4 Reorder the terms: 4 + 4r + r2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + 4r + r2 = 27 Factor a perfect square on the left side: (r + 2)(r + 2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (r + 2) equal to 5.196152423 and -5.196152423.Subproblem 1
r + 2 = 5.196152423 Simplifying r + 2 = 5.196152423 Reorder the terms: 2 + r = 5.196152423 Solving 2 + r = 5.196152423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + r = 5.196152423 + -2 r = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 r = 3.196152423 Simplifying r = 3.196152423Subproblem 2
r + 2 = -5.196152423 Simplifying r + 2 = -5.196152423 Reorder the terms: 2 + r = -5.196152423 Solving 2 + r = -5.196152423 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + r = -5.196152423 + -2 r = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 r = -7.196152423 Simplifying r = -7.196152423Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.196152423, -7.196152423}
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