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Simplifying 4m5 + 6m3 + -8m = 0 Reorder the terms: -8m + 6m3 + 4m5 = 0 Solving -8m + 6m3 + 4m5 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m'. 2m(-4 + 3m2 + 2m4) = 0 Ignore the factor 2.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 + 3m2 + 2m4)' equal to zero and attempt to solve: Simplifying -4 + 3m2 + 2m4 = 0 Solving -4 + 3m2 + 2m4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 1.5m2 + m4 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.5m2 + 2 + m4 = 0 + 2 Reorder the terms: -2 + 2 + 1.5m2 + m4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.5m2 + m4 = 0 + 2 1.5m2 + m4 = 0 + 2 Combine like terms: 0 + 2 = 2 1.5m2 + m4 = 2 The m term is 1.5m2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5m2 + 0.5625 + m4 = 2 + 0.5625 Reorder the terms: 0.5625 + 1.5m2 + m4 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + 1.5m2 + m4 = 2.5625 Factor a perfect square on the left side: (m2 + 0.75)(m2 + 0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (m2 + 0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
m2 + 0.75 = 1.600781059 Simplifying m2 + 0.75 = 1.600781059 Reorder the terms: 0.75 + m2 = 1.600781059 Solving 0.75 + m2 = 1.600781059 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = 1.600781059 + -0.75 m2 = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 m2 = 0.850781059 Simplifying m2 = 0.850781059 Take the square root of each side: m = {-0.922377937, 0.922377937}Subproblem 2
m2 + 0.75 = -1.600781059 Simplifying m2 + 0.75 = -1.600781059 Reorder the terms: 0.75 + m2 = -1.600781059 Solving 0.75 + m2 = -1.600781059 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = -1.600781059 + -0.75 m2 = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 m2 = -2.350781059 Simplifying m2 = -2.350781059 Reorder the terms: 2.350781059 + m2 = -2.350781059 + 2.350781059 Combine like terms: -2.350781059 + 2.350781059 = 0.000000000 2.350781059 + m2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
m = {0}
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