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Simplifying m3 + 6m2 + -4m = 0 Reorder the terms: -4m + 6m2 + m3 = 0 Solving -4m + 6m2 + m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(-4 + 6m + 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 '(-4 + 6m + m2)' equal to zero and attempt to solve: Simplifying -4 + 6m + m2 = 0 Solving -4 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + 6m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6m + m2 = 0 + 4 6m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 6m + m2 = 4 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 = 4 + 9 Reorder the terms: 9 + 6m + m2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6m + m2 = 13 Factor a perfect square on the left side: (m + 3)(m + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (m + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
m + 3 = 3.605551275 Simplifying m + 3 = 3.605551275 Reorder the terms: 3 + m = 3.605551275 Solving 3 + m = 3.605551275 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 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + m = 3.605551275 + -3 m = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 m = 0.605551275 Simplifying m = 0.605551275Subproblem 2
m + 3 = -3.605551275 Simplifying m + 3 = -3.605551275 Reorder the terms: 3 + m = -3.605551275 Solving 3 + m = -3.605551275 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 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + m = -3.605551275 + -3 m = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 m = -6.605551275 Simplifying m = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.605551275, -6.605551275}Solution
m = {0, 0.605551275, -6.605551275}
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