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Simplifying 3m + 5m(6 + -1m) = 4 3m + (6 * 5m + -1m * 5m) = 4 3m + (30m + -5m2) = 4 Combine like terms: 3m + 30m = 33m 33m + -5m2 = 4 Solving 33m + -5m2 = 4 Solving for variable 'm'. Reorder the terms: -4 + 33m + -5m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 33m + -5m2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.8 + -6.6m + m2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -6.6m + -0.8 + m2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -6.6m + m2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -6.6m + m2 = 0 + -0.8 -6.6m + m2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -6.6m + m2 = -0.8 The m term is -6.6m. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6m + 10.89 + m2 = -0.8 + 10.89 Reorder the terms: 10.89 + -6.6m + m2 = -0.8 + 10.89 Combine like terms: -0.8 + 10.89 = 10.09 10.89 + -6.6m + m2 = 10.09 Factor a perfect square on the left side: (m + -3.3)(m + -3.3) = 10.09 Calculate the square root of the right side: 3.176476035 Break this problem into two subproblems by setting (m + -3.3) equal to 3.176476035 and -3.176476035.Subproblem 1
m + -3.3 = 3.176476035 Simplifying m + -3.3 = 3.176476035 Reorder the terms: -3.3 + m = 3.176476035 Solving -3.3 + m = 3.176476035 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + m = 3.176476035 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + m = 3.176476035 + 3.3 m = 3.176476035 + 3.3 Combine like terms: 3.176476035 + 3.3 = 6.476476035 m = 6.476476035 Simplifying m = 6.476476035Subproblem 2
m + -3.3 = -3.176476035 Simplifying m + -3.3 = -3.176476035 Reorder the terms: -3.3 + m = -3.176476035 Solving -3.3 + m = -3.176476035 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + m = -3.176476035 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + m = -3.176476035 + 3.3 m = -3.176476035 + 3.3 Combine like terms: -3.176476035 + 3.3 = 0.123523965 m = 0.123523965 Simplifying m = 0.123523965Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.476476035, 0.123523965}
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