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Simplifying (3r + -13)(r + 14) = -44 Reorder the terms: (-13 + 3r)(r + 14) = -44 Reorder the terms: (-13 + 3r)(14 + r) = -44 Multiply (-13 + 3r) * (14 + r) (-13(14 + r) + 3r * (14 + r)) = -44 ((14 * -13 + r * -13) + 3r * (14 + r)) = -44 ((-182 + -13r) + 3r * (14 + r)) = -44 (-182 + -13r + (14 * 3r + r * 3r)) = -44 (-182 + -13r + (42r + 3r2)) = -44 Combine like terms: -13r + 42r = 29r (-182 + 29r + 3r2) = -44 Solving -182 + 29r + 3r2 = -44 Solving for variable 'r'. Reorder the terms: -182 + 44 + 29r + 3r2 = -44 + 44 Combine like terms: -182 + 44 = -138 -138 + 29r + 3r2 = -44 + 44 Combine like terms: -44 + 44 = 0 -138 + 29r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -46 + 9.666666667r + r2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + 9.666666667r + 46 + r2 = 0 + 46 Reorder the terms: -46 + 46 + 9.666666667r + r2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 9.666666667r + r2 = 0 + 46 9.666666667r + r2 = 0 + 46 Combine like terms: 0 + 46 = 46 9.666666667r + r2 = 46 The r term is 9.666666667r. Take half its coefficient (4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. 9.666666667r + 23.36111112 + r2 = 46 + 23.36111112 Reorder the terms: 23.36111112 + 9.666666667r + r2 = 46 + 23.36111112 Combine like terms: 46 + 23.36111112 = 69.36111112 23.36111112 + 9.666666667r + r2 = 69.36111112 Factor a perfect square on the left side: (r + 4.833333334)(r + 4.833333334) = 69.36111112 Calculate the square root of the right side: 8.328331833 Break this problem into two subproblems by setting (r + 4.833333334) equal to 8.328331833 and -8.328331833.Subproblem 1
r + 4.833333334 = 8.328331833 Simplifying r + 4.833333334 = 8.328331833 Reorder the terms: 4.833333334 + r = 8.328331833 Solving 4.833333334 + r = 8.328331833 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + r = 8.328331833 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + r = 8.328331833 + -4.833333334 r = 8.328331833 + -4.833333334 Combine like terms: 8.328331833 + -4.833333334 = 3.494998499 r = 3.494998499 Simplifying r = 3.494998499Subproblem 2
r + 4.833333334 = -8.328331833 Simplifying r + 4.833333334 = -8.328331833 Reorder the terms: 4.833333334 + r = -8.328331833 Solving 4.833333334 + r = -8.328331833 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + r = -8.328331833 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + r = -8.328331833 + -4.833333334 r = -8.328331833 + -4.833333334 Combine like terms: -8.328331833 + -4.833333334 = -13.161665167 r = -13.161665167 Simplifying r = -13.161665167Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.494998499, -13.161665167}
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