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Simplifying m3 + 16m2 + 24m = 0 Reorder the terms: 24m + 16m2 + m3 = 0 Solving 24m + 16m2 + m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(24 + 16m + m2) = 0Subproblem 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 '(24 + 16m + m2)' equal to zero and attempt to solve: Simplifying 24 + 16m + m2 = 0 Solving 24 + 16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 16m + -24 + m2 = 0 + -24 Reorder the terms: 24 + -24 + 16m + m2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 16m + m2 = 0 + -24 16m + m2 = 0 + -24 Combine like terms: 0 + -24 = -24 16m + m2 = -24 The m term is 16m. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16m + 64 + m2 = -24 + 64 Reorder the terms: 64 + 16m + m2 = -24 + 64 Combine like terms: -24 + 64 = 40 64 + 16m + m2 = 40 Factor a perfect square on the left side: (m + 8)(m + 8) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (m + 8) equal to 6.32455532 and -6.32455532.Subproblem 1
m + 8 = 6.32455532 Simplifying m + 8 = 6.32455532 Reorder the terms: 8 + m = 6.32455532 Solving 8 + m = 6.32455532 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = 6.32455532 + -8 Combine like terms: 8 + -8 = 0 0 + m = 6.32455532 + -8 m = 6.32455532 + -8 Combine like terms: 6.32455532 + -8 = -1.67544468 m = -1.67544468 Simplifying m = -1.67544468Subproblem 2
m + 8 = -6.32455532 Simplifying m + 8 = -6.32455532 Reorder the terms: 8 + m = -6.32455532 Solving 8 + m = -6.32455532 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = -6.32455532 + -8 Combine like terms: 8 + -8 = 0 0 + m = -6.32455532 + -8 m = -6.32455532 + -8 Combine like terms: -6.32455532 + -8 = -14.32455532 m = -14.32455532 Simplifying m = -14.32455532Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.67544468, -14.32455532}Solution
m = {0, -1.67544468, -14.32455532}
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