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Simplifying 6m3 + -12m + -24m2 = 0 Reorder the terms: -12m + -24m2 + 6m3 = 0 Solving -12m + -24m2 + 6m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '6m'. 6m(-2 + -4m + m2) = 0 Ignore the factor 6.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 '(-2 + -4m + m2)' equal to zero and attempt to solve: Simplifying -2 + -4m + m2 = 0 Solving -2 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -4m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4m + m2 = 0 + 2 -4m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4m + m2 = 2 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 2 + 4 Reorder the terms: 4 + -4m + m2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4m + m2 = 6 Factor a perfect square on the left side: (m + -2)(m + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
m + -2 = 2.449489743 Simplifying m + -2 = 2.449489743 Reorder the terms: -2 + m = 2.449489743 Solving -2 + m = 2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + m = 2.449489743 + 2 m = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 m = 4.449489743 Simplifying m = 4.449489743Subproblem 2
m + -2 = -2.449489743 Simplifying m + -2 = -2.449489743 Reorder the terms: -2 + m = -2.449489743 Solving -2 + m = -2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + m = -2.449489743 + 2 m = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 m = -0.449489743 Simplifying m = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.449489743, -0.449489743}Solution
m = {0, 4.449489743, -0.449489743}
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