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Simplifying 3m(1 + -1m) = 2(3m + -1) (1 * 3m + -1m * 3m) = 2(3m + -1) (3m + -3m2) = 2(3m + -1) Reorder the terms: 3m + -3m2 = 2(-1 + 3m) 3m + -3m2 = (-1 * 2 + 3m * 2) 3m + -3m2 = (-2 + 6m) Solving 3m + -3m2 = -2 + 6m Solving for variable 'm'. Reorder the terms: 2 + 3m + -6m + -3m2 = -2 + 6m + 2 + -6m Combine like terms: 3m + -6m = -3m 2 + -3m + -3m2 = -2 + 6m + 2 + -6m Reorder the terms: 2 + -3m + -3m2 = -2 + 2 + 6m + -6m Combine like terms: -2 + 2 = 0 2 + -3m + -3m2 = 0 + 6m + -6m 2 + -3m + -3m2 = 6m + -6m Combine like terms: 6m + -6m = 0 2 + -3m + -3m2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + m + m2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + m + 0.6666666667 + m2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + m + m2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + m + m2 = 0 + 0.6666666667 m + m2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 m + m2 = 0.6666666667 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 0.6666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 1.25 + m2 = 0.9166666667 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (m + 0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
m + 0.5 = 0.957427108 Simplifying m + 0.5 = 0.957427108 Reorder the terms: 0.5 + m = 0.957427108 Solving 0.5 + m = 0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.957427108 + -0.5 m = 0.957427108 + -0.5 Combine like terms: 0.957427108 + -0.5 = 0.457427108 m = 0.457427108 Simplifying m = 0.457427108Subproblem 2
m + 0.5 = -0.957427108 Simplifying m + 0.5 = -0.957427108 Reorder the terms: 0.5 + m = -0.957427108 Solving 0.5 + m = -0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.957427108 + -0.5 m = -0.957427108 + -0.5 Combine like terms: -0.957427108 + -0.5 = -1.457427108 m = -1.457427108 Simplifying m = -1.457427108Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.457427108, -1.457427108}
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