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Simplifying 2m(-1m + 6) = 3 Reorder the terms: 2m(6 + -1m) = 3 (6 * 2m + -1m * 2m) = 3 (12m + -2m2) = 3 Solving 12m + -2m2 = 3 Solving for variable 'm'. Reorder the terms: -3 + 12m + -2m2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 12m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -6m + m2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -6m + -1.5 + m2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -6m + m2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -6m + m2 = 0 + -1.5 -6m + m2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -6m + m2 = -1.5 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = -1.5 + 9 Reorder the terms: 9 + -6m + m2 = -1.5 + 9 Combine like terms: -1.5 + 9 = 7.5 9 + -6m + m2 = 7.5 Factor a perfect square on the left side: (m + -3)(m + -3) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (m + -3) equal to 2.738612788 and -2.738612788.Subproblem 1
m + -3 = 2.738612788 Simplifying m + -3 = 2.738612788 Reorder the terms: -3 + m = 2.738612788 Solving -3 + m = 2.738612788 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 2.738612788 + 3 Combine like terms: -3 + 3 = 0 0 + m = 2.738612788 + 3 m = 2.738612788 + 3 Combine like terms: 2.738612788 + 3 = 5.738612788 m = 5.738612788 Simplifying m = 5.738612788Subproblem 2
m + -3 = -2.738612788 Simplifying m + -3 = -2.738612788 Reorder the terms: -3 + m = -2.738612788 Solving -3 + m = -2.738612788 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -2.738612788 + 3 Combine like terms: -3 + 3 = 0 0 + m = -2.738612788 + 3 m = -2.738612788 + 3 Combine like terms: -2.738612788 + 3 = 0.261387212 m = 0.261387212 Simplifying m = 0.261387212Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.738612788, 0.261387212}
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