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Simplifying (m + -1)(m + 9) = 8 Reorder the terms: (-1 + m)(m + 9) = 8 Reorder the terms: (-1 + m)(9 + m) = 8 Multiply (-1 + m) * (9 + m) (-1(9 + m) + m(9 + m)) = 8 ((9 * -1 + m * -1) + m(9 + m)) = 8 ((-9 + -1m) + m(9 + m)) = 8 (-9 + -1m + (9 * m + m * m)) = 8 (-9 + -1m + (9m + m2)) = 8 Combine like terms: -1m + 9m = 8m (-9 + 8m + m2) = 8 Solving -9 + 8m + m2 = 8 Solving for variable 'm'. Reorder the terms: -9 + -8 + 8m + m2 = 8 + -8 Combine like terms: -9 + -8 = -17 -17 + 8m + m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -17 + 8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 8m + 17 + m2 = 0 + 17 Reorder the terms: -17 + 17 + 8m + m2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 8m + m2 = 0 + 17 8m + m2 = 0 + 17 Combine like terms: 0 + 17 = 17 8m + m2 = 17 The m term is 8m. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8m + 16 + m2 = 17 + 16 Reorder the terms: 16 + 8m + m2 = 17 + 16 Combine like terms: 17 + 16 = 33 16 + 8m + m2 = 33 Factor a perfect square on the left side: (m + 4)(m + 4) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (m + 4) equal to 5.744562647 and -5.744562647.Subproblem 1
m + 4 = 5.744562647 Simplifying m + 4 = 5.744562647 Reorder the terms: 4 + m = 5.744562647 Solving 4 + m = 5.744562647 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = 5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + m = 5.744562647 + -4 m = 5.744562647 + -4 Combine like terms: 5.744562647 + -4 = 1.744562647 m = 1.744562647 Simplifying m = 1.744562647Subproblem 2
m + 4 = -5.744562647 Simplifying m + 4 = -5.744562647 Reorder the terms: 4 + m = -5.744562647 Solving 4 + m = -5.744562647 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = -5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + m = -5.744562647 + -4 m = -5.744562647 + -4 Combine like terms: -5.744562647 + -4 = -9.744562647 m = -9.744562647 Simplifying m = -9.744562647Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.744562647, -9.744562647}
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