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Simplifying (m + -2)(m + -6) = 7 Reorder the terms: (-2 + m)(m + -6) = 7 Reorder the terms: (-2 + m)(-6 + m) = 7 Multiply (-2 + m) * (-6 + m) (-2(-6 + m) + m(-6 + m)) = 7 ((-6 * -2 + m * -2) + m(-6 + m)) = 7 ((12 + -2m) + m(-6 + m)) = 7 (12 + -2m + (-6 * m + m * m)) = 7 (12 + -2m + (-6m + m2)) = 7 Combine like terms: -2m + -6m = -8m (12 + -8m + m2) = 7 Solving 12 + -8m + m2 = 7 Solving for variable 'm'. Reorder the terms: 12 + -7 + -8m + m2 = 7 + -7 Combine like terms: 12 + -7 = 5 5 + -8m + m2 = 7 + -7 Combine like terms: 7 + -7 = 0 5 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + -8m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8m + m2 = 0 + -5 -8m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8m + m2 = -5 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 = -5 + 16 Reorder the terms: 16 + -8m + m2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8m + m2 = 11 Factor a perfect square on the left side: (m + -4)(m + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -4 = 3.31662479 Simplifying m + -4 = 3.31662479 Reorder the terms: -4 + m = 3.31662479 Solving -4 + m = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.31662479 + 4 m = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 m = 7.31662479 Simplifying m = 7.31662479Subproblem 2
m + -4 = -3.31662479 Simplifying m + -4 = -3.31662479 Reorder the terms: -4 + m = -3.31662479 Solving -4 + m = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.31662479 + 4 m = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 m = 0.68337521 Simplifying m = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.31662479, 0.68337521}
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