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Simplifying 6m3 + -12m2 + -24m = 0 Reorder the terms: -24m + -12m2 + 6m3 = 0 Solving -24m + -12m2 + 6m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '6m'. 6m(-4 + -2m + 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 '(-4 + -2m + m2)' equal to zero and attempt to solve: Simplifying -4 + -2m + m2 = 0 Solving -4 + -2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + -2m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2m + m2 = 0 + 4 -2m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2m + m2 = 4 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 4 + 1 Reorder the terms: 1 + -2m + m2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2m + m2 = 5 Factor a perfect square on the left side: (m + -1)(m + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
m + -1 = 2.236067978 Simplifying m + -1 = 2.236067978 Reorder the terms: -1 + m = 2.236067978 Solving -1 + m = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.236067978 + 1 m = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 m = 3.236067978 Simplifying m = 3.236067978Subproblem 2
m + -1 = -2.236067978 Simplifying m + -1 = -2.236067978 Reorder the terms: -1 + m = -2.236067978 Solving -1 + m = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.236067978 + 1 m = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 m = -1.236067978 Simplifying m = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.236067978, -1.236067978}Solution
m = {0, 3.236067978, -1.236067978}
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