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Simplifying 3m6 + 30m4 + -30m2 = 0 Reorder the terms: -30m2 + 30m4 + 3m6 = 0 Solving -30m2 + 30m4 + 3m6 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m2'. 3m2(-10 + 10m2 + m4) = 0 Ignore the factor 3.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 '(-10 + 10m2 + m4)' equal to zero and attempt to solve: Simplifying -10 + 10m2 + m4 = 0 Solving -10 + 10m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 10m2 + 10 + m4 = 0 + 10 Reorder the terms: -10 + 10 + 10m2 + m4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10m2 + m4 = 0 + 10 10m2 + m4 = 0 + 10 Combine like terms: 0 + 10 = 10 10m2 + m4 = 10 The m term is 10m2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m2 + 25 + m4 = 10 + 25 Reorder the terms: 25 + 10m2 + m4 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10m2 + m4 = 35 Factor a perfect square on the left side: (m2 + 5)(m2 + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (m2 + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
m2 + 5 = 5.916079783 Simplifying m2 + 5 = 5.916079783 Reorder the terms: 5 + m2 = 5.916079783 Solving 5 + m2 = 5.916079783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m2 = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + m2 = 5.916079783 + -5 m2 = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 m2 = 0.916079783 Simplifying m2 = 0.916079783 Take the square root of each side: m = {-0.957120569, 0.957120569}Subproblem 2
m2 + 5 = -5.916079783 Simplifying m2 + 5 = -5.916079783 Reorder the terms: 5 + m2 = -5.916079783 Solving 5 + m2 = -5.916079783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m2 = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + m2 = -5.916079783 + -5 m2 = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 m2 = -10.916079783 Simplifying m2 = -10.916079783 Reorder the terms: 10.916079783 + m2 = -10.916079783 + 10.916079783 Combine like terms: -10.916079783 + 10.916079783 = 0.000000000 10.916079783 + 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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