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Simplifying 5m(m + -3) + 6(m + -7) = 0 Reorder the terms: 5m(-3 + m) + 6(m + -7) = 0 (-3 * 5m + m * 5m) + 6(m + -7) = 0 (-15m + 5m2) + 6(m + -7) = 0 Reorder the terms: -15m + 5m2 + 6(-7 + m) = 0 -15m + 5m2 + (-7 * 6 + m * 6) = 0 -15m + 5m2 + (-42 + 6m) = 0 Reorder the terms: -42 + -15m + 6m + 5m2 = 0 Combine like terms: -15m + 6m = -9m -42 + -9m + 5m2 = 0 Solving -42 + -9m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.4 + -1.8m + m2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + -1.8m + 8.4 + m2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + -1.8m + m2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + -1.8m + m2 = 0 + 8.4 -1.8m + m2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 -1.8m + m2 = 8.4 The m term is -1.8m. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8m + 0.81 + m2 = 8.4 + 0.81 Reorder the terms: 0.81 + -1.8m + m2 = 8.4 + 0.81 Combine like terms: 8.4 + 0.81 = 9.21 0.81 + -1.8m + m2 = 9.21 Factor a perfect square on the left side: (m + -0.9)(m + -0.9) = 9.21 Calculate the square root of the right side: 3.034798181 Break this problem into two subproblems by setting (m + -0.9) equal to 3.034798181 and -3.034798181.Subproblem 1
m + -0.9 = 3.034798181 Simplifying m + -0.9 = 3.034798181 Reorder the terms: -0.9 + m = 3.034798181 Solving -0.9 + m = 3.034798181 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = 3.034798181 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = 3.034798181 + 0.9 m = 3.034798181 + 0.9 Combine like terms: 3.034798181 + 0.9 = 3.934798181 m = 3.934798181 Simplifying m = 3.934798181Subproblem 2
m + -0.9 = -3.034798181 Simplifying m + -0.9 = -3.034798181 Reorder the terms: -0.9 + m = -3.034798181 Solving -0.9 + m = -3.034798181 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = -3.034798181 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = -3.034798181 + 0.9 m = -3.034798181 + 0.9 Combine like terms: -3.034798181 + 0.9 = -2.134798181 m = -2.134798181 Simplifying m = -2.134798181Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.934798181, -2.134798181}
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