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Simplifying (r + -4)(r + 12) = -37 Reorder the terms: (-4 + r)(r + 12) = -37 Reorder the terms: (-4 + r)(12 + r) = -37 Multiply (-4 + r) * (12 + r) (-4(12 + r) + r(12 + r)) = -37 ((12 * -4 + r * -4) + r(12 + r)) = -37 ((-48 + -4r) + r(12 + r)) = -37 (-48 + -4r + (12 * r + r * r)) = -37 (-48 + -4r + (12r + r2)) = -37 Combine like terms: -4r + 12r = 8r (-48 + 8r + r2) = -37 Solving -48 + 8r + r2 = -37 Solving for variable 'r'. Reorder the terms: -48 + 37 + 8r + r2 = -37 + 37 Combine like terms: -48 + 37 = -11 -11 + 8r + r2 = -37 + 37 Combine like terms: -37 + 37 = 0 -11 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 8r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 8r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 8r + r2 = 0 + 11 8r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 8r + r2 = 11 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 = 11 + 16 Reorder the terms: 16 + 8r + r2 = 11 + 16 Combine like terms: 11 + 16 = 27 16 + 8r + r2 = 27 Factor a perfect square on the left side: (r + 4)(r + 4) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (r + 4) equal to 5.196152423 and -5.196152423.Subproblem 1
r + 4 = 5.196152423 Simplifying r + 4 = 5.196152423 Reorder the terms: 4 + r = 5.196152423 Solving 4 + r = 5.196152423 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 = 5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + r = 5.196152423 + -4 r = 5.196152423 + -4 Combine like terms: 5.196152423 + -4 = 1.196152423 r = 1.196152423 Simplifying r = 1.196152423Subproblem 2
r + 4 = -5.196152423 Simplifying r + 4 = -5.196152423 Reorder the terms: 4 + r = -5.196152423 Solving 4 + r = -5.196152423 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 = -5.196152423 + -4 Combine like terms: 4 + -4 = 0 0 + r = -5.196152423 + -4 r = -5.196152423 + -4 Combine like terms: -5.196152423 + -4 = -9.196152423 r = -9.196152423 Simplifying r = -9.196152423Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.196152423, -9.196152423}
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