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Simplifying 8m4 + 6m3 + -12m2 = 0 Reorder the terms: -12m2 + 6m3 + 8m4 = 0 Solving -12m2 + 6m3 + 8m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m2'. 2m2(-6 + 3m + 4m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(-6 + 3m + 4m2)' equal to zero and attempt to solve: Simplifying -6 + 3m + 4m2 = 0 Solving -6 + 3m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 0.75m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.75m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.75m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.75m + m2 = 0 + 1.5 0.75m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.75m + m2 = 1.5 The m term is 0.75m. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75m + 0.140625 + m2 = 1.5 + 0.140625 Reorder the terms: 0.140625 + 0.75m + m2 = 1.5 + 0.140625 Combine like terms: 1.5 + 0.140625 = 1.640625 0.140625 + 0.75m + m2 = 1.640625 Factor a perfect square on the left side: (m + 0.375)(m + 0.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (m + 0.375) equal to 1.280868846 and -1.280868846.Subproblem 1
m + 0.375 = 1.280868846 Simplifying m + 0.375 = 1.280868846 Reorder the terms: 0.375 + m = 1.280868846 Solving 0.375 + m = 1.280868846 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = 1.280868846 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = 1.280868846 + -0.375 m = 1.280868846 + -0.375 Combine like terms: 1.280868846 + -0.375 = 0.905868846 m = 0.905868846 Simplifying m = 0.905868846Subproblem 2
m + 0.375 = -1.280868846 Simplifying m + 0.375 = -1.280868846 Reorder the terms: 0.375 + m = -1.280868846 Solving 0.375 + m = -1.280868846 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = -1.280868846 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = -1.280868846 + -0.375 m = -1.280868846 + -0.375 Combine like terms: -1.280868846 + -0.375 = -1.655868846 m = -1.655868846 Simplifying m = -1.655868846Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.905868846, -1.655868846}Solution
m = {0, 0.905868846, -1.655868846}
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