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Simplifying 3(5m + -4) * m = -2 Reorder the terms: 3(-4 + 5m) * m = -2 Reorder the terms for easier multiplication: 3m(-4 + 5m) = -2 (-4 * 3m + 5m * 3m) = -2 (-12m + 15m2) = -2 Solving -12m + 15m2 = -2 Solving for variable 'm'. Reorder the terms: 2 + -12m + 15m2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -12m + 15m2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + -0.8m + m2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + -0.8m + -0.1333333333 + m2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + -0.8m + m2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + -0.8m + m2 = 0 + -0.1333333333 -0.8m + m2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 -0.8m + m2 = -0.1333333333 The m term is -0.8m. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8m + 0.16 + m2 = -0.1333333333 + 0.16 Reorder the terms: 0.16 + -0.8m + m2 = -0.1333333333 + 0.16 Combine like terms: -0.1333333333 + 0.16 = 0.0266666667 0.16 + -0.8m + m2 = 0.0266666667 Factor a perfect square on the left side: (m + -0.4)(m + -0.4) = 0.0266666667 Calculate the square root of the right side: 0.163299316 Break this problem into two subproblems by setting (m + -0.4) equal to 0.163299316 and -0.163299316.Subproblem 1
m + -0.4 = 0.163299316 Simplifying m + -0.4 = 0.163299316 Reorder the terms: -0.4 + m = 0.163299316 Solving -0.4 + m = 0.163299316 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = 0.163299316 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = 0.163299316 + 0.4 m = 0.163299316 + 0.4 Combine like terms: 0.163299316 + 0.4 = 0.563299316 m = 0.563299316 Simplifying m = 0.563299316Subproblem 2
m + -0.4 = -0.163299316 Simplifying m + -0.4 = -0.163299316 Reorder the terms: -0.4 + m = -0.163299316 Solving -0.4 + m = -0.163299316 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = -0.163299316 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = -0.163299316 + 0.4 m = -0.163299316 + 0.4 Combine like terms: -0.163299316 + 0.4 = 0.236700684 m = 0.236700684 Simplifying m = 0.236700684Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.563299316, 0.236700684}
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