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Simplifying 40m5 + 24m3 + -3m = 0 Reorder the terms: -3m + 24m3 + 40m5 = 0 Solving -3m + 24m3 + 40m5 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(-3 + 24m2 + 40m4) = 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 '(-3 + 24m2 + 40m4)' equal to zero and attempt to solve: Simplifying -3 + 24m2 + 40m4 = 0 Solving -3 + 24m2 + 40m4 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.075 + 0.6m2 + m4 = 0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + 0.6m2 + 0.075 + m4 = 0 + 0.075 Reorder the terms: -0.075 + 0.075 + 0.6m2 + m4 = 0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + 0.6m2 + m4 = 0 + 0.075 0.6m2 + m4 = 0 + 0.075 Combine like terms: 0 + 0.075 = 0.075 0.6m2 + m4 = 0.075 The m term is 0.6m2. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6m2 + 0.09 + m4 = 0.075 + 0.09 Reorder the terms: 0.09 + 0.6m2 + m4 = 0.075 + 0.09 Combine like terms: 0.075 + 0.09 = 0.165 0.09 + 0.6m2 + m4 = 0.165 Factor a perfect square on the left side: (m2 + 0.3)(m2 + 0.3) = 0.165 Calculate the square root of the right side: 0.40620192 Break this problem into two subproblems by setting (m2 + 0.3) equal to 0.40620192 and -0.40620192.Subproblem 1
m2 + 0.3 = 0.40620192 Simplifying m2 + 0.3 = 0.40620192 Reorder the terms: 0.3 + m2 = 0.40620192 Solving 0.3 + m2 = 0.40620192 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + m2 = 0.40620192 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m2 = 0.40620192 + -0.3 m2 = 0.40620192 + -0.3 Combine like terms: 0.40620192 + -0.3 = 0.10620192 m2 = 0.10620192 Simplifying m2 = 0.10620192 Take the square root of each side: m = {-0.325886361, 0.325886361}Subproblem 2
m2 + 0.3 = -0.40620192 Simplifying m2 + 0.3 = -0.40620192 Reorder the terms: 0.3 + m2 = -0.40620192 Solving 0.3 + m2 = -0.40620192 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + m2 = -0.40620192 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m2 = -0.40620192 + -0.3 m2 = -0.40620192 + -0.3 Combine like terms: -0.40620192 + -0.3 = -0.70620192 m2 = -0.70620192 Simplifying m2 = -0.70620192 Reorder the terms: 0.70620192 + m2 = -0.70620192 + 0.70620192 Combine like terms: -0.70620192 + 0.70620192 = 0.00000000 0.70620192 + m2 = 0.00000000 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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