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Simplifying 5m(m2 + -6m + 3) = 0 Reorder the terms: 5m(3 + -6m + m2) = 0 (3 * 5m + -6m * 5m + m2 * 5m) = 0 (15m + -30m2 + 5m3) = 0 Solving 15m + -30m2 + 5m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '5m'. 5m(3 + -6m + m2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(3 + -6m + m2)' equal to zero and attempt to solve: Simplifying 3 + -6m + m2 = 0 Solving 3 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6m + -3 + m2 = 0 + -3 Reorder the terms: 3 + -3 + -6m + m2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6m + m2 = 0 + -3 -6m + m2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6m + m2 = -3 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 = -3 + 9 Reorder the terms: 9 + -6m + m2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6m + m2 = 6 Factor a perfect square on the left side: (m + -3)(m + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
m + -3 = 2.449489743 Simplifying m + -3 = 2.449489743 Reorder the terms: -3 + m = 2.449489743 Solving -3 + m = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + m = 2.449489743 + 3 m = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 m = 5.449489743 Simplifying m = 5.449489743Subproblem 2
m + -3 = -2.449489743 Simplifying m + -3 = -2.449489743 Reorder the terms: -3 + m = -2.449489743 Solving -3 + m = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + m = -2.449489743 + 3 m = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 m = 0.550510257 Simplifying m = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.449489743, 0.550510257}Solution
m = {0, 5.449489743, 0.550510257}
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