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Simplifying ((m + -1) + -2)((2m + 8) + -5) + -1(-2(-2)) = 0 Reorder the terms: ((-1 + m) + -2)((2m + 8) + -5) + -1(-2(-2)) = 0 Remove parenthesis around (-1 + m) (-1 + m + -2)((2m + 8) + -5) + -1(-2(-2)) = 0 Reorder the terms: (-1 + -2 + m)((2m + 8) + -5) + -1(-2(-2)) = 0 Combine like terms: -1 + -2 = -3 (-3 + m)((2m + 8) + -5) + -1(-2(-2)) = 0 Reorder the terms: (-3 + m)((8 + 2m) + -5) + -1(-2(-2)) = 0 Remove parenthesis around (8 + 2m) (-3 + m)(8 + 2m + -5) + -1(-2(-2)) = 0 Reorder the terms: (-3 + m)(8 + -5 + 2m) + -1(-2(-2)) = 0 Combine like terms: 8 + -5 = 3 (-3 + m)(3 + 2m) + -1(-2(-2)) = 0 Multiply (-3 + m) * (3 + 2m) (-3(3 + 2m) + m(3 + 2m)) + -1(-2(-2)) = 0 ((3 * -3 + 2m * -3) + m(3 + 2m)) + -1(-2(-2)) = 0 ((-9 + -6m) + m(3 + 2m)) + -1(-2(-2)) = 0 (-9 + -6m + (3 * m + 2m * m)) + -1(-2(-2)) = 0 (-9 + -6m + (3m + 2m2)) + -1(-2(-2)) = 0 Combine like terms: -6m + 3m = -3m (-9 + -3m + 2m2) + -1(-2(-2)) = 0 Multiply -2 * -2 -9 + -3m + 2m2 + -1(4) = 0 Multiply -1 * 4 -9 + -3m + 2m2 + -4 = 0 Reorder the terms: -9 + -4 + -3m + 2m2 = 0 Combine like terms: -9 + -4 = -13 -13 + -3m + 2m2 = 0 Solving -13 + -3m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -1.5m + m2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1.5m + 6.5 + m2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1.5m + m2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1.5m + m2 = 0 + 6.5 -1.5m + m2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1.5m + m2 = 6.5 The m term is -1.5m. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5m + 0.5625 + m2 = 6.5 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 6.5 + 0.5625 Combine like terms: 6.5 + 0.5625 = 7.0625 0.5625 + -1.5m + m2 = 7.0625 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (m + -0.75) equal to 2.657536453 and -2.657536453.Subproblem 1
m + -0.75 = 2.657536453 Simplifying m + -0.75 = 2.657536453 Reorder the terms: -0.75 + m = 2.657536453 Solving -0.75 + m = 2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 2.657536453 + 0.75 m = 2.657536453 + 0.75 Combine like terms: 2.657536453 + 0.75 = 3.407536453 m = 3.407536453 Simplifying m = 3.407536453Subproblem 2
m + -0.75 = -2.657536453 Simplifying m + -0.75 = -2.657536453 Reorder the terms: -0.75 + m = -2.657536453 Solving -0.75 + m = -2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -2.657536453 + 0.75 m = -2.657536453 + 0.75 Combine like terms: -2.657536453 + 0.75 = -1.907536453 m = -1.907536453 Simplifying m = -1.907536453Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.407536453, -1.907536453}
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