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Simplifying 3(m + -3)(m + -2) = 3m Reorder the terms: 3(-3 + m)(m + -2) = 3m Reorder the terms: 3(-3 + m)(-2 + m) = 3m Multiply (-3 + m) * (-2 + m) 3(-3(-2 + m) + m(-2 + m)) = 3m 3((-2 * -3 + m * -3) + m(-2 + m)) = 3m 3((6 + -3m) + m(-2 + m)) = 3m 3(6 + -3m + (-2 * m + m * m)) = 3m 3(6 + -3m + (-2m + m2)) = 3m Combine like terms: -3m + -2m = -5m 3(6 + -5m + m2) = 3m (6 * 3 + -5m * 3 + m2 * 3) = 3m (18 + -15m + 3m2) = 3m Solving 18 + -15m + 3m2 = 3m Solving for variable 'm'. Reorder the terms: 18 + -15m + -3m + 3m2 = 3m + -3m Combine like terms: -15m + -3m = -18m 18 + -18m + 3m2 = 3m + -3m Combine like terms: 3m + -3m = 0 18 + -18m + 3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -6m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -6m + m2)' equal to zero and attempt to solve: Simplifying 6 + -6m + m2 = 0 Solving 6 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6m + -6 + m2 = 0 + -6 Reorder the terms: 6 + -6 + -6m + m2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6m + m2 = 0 + -6 -6m + m2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6m + m2 = -6 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 = -6 + 9 Reorder the terms: 9 + -6m + m2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6m + m2 = 3 Factor a perfect square on the left side: (m + -3)(m + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (m + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
m + -3 = 1.732050808 Simplifying m + -3 = 1.732050808 Reorder the terms: -3 + m = 1.732050808 Solving -3 + m = 1.732050808 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 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + m = 1.732050808 + 3 m = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 m = 4.732050808 Simplifying m = 4.732050808Subproblem 2
m + -3 = -1.732050808 Simplifying m + -3 = -1.732050808 Reorder the terms: -3 + m = -1.732050808 Solving -3 + m = -1.732050808 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 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + m = -1.732050808 + 3 m = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 m = 1.267949192 Simplifying m = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.732050808, 1.267949192}Solution
m = {4.732050808, 1.267949192}
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