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Simplifying 3m2 + 30m6 + 30m4 = 0 Reorder the terms: 3m2 + 30m4 + 30m6 = 0 Solving 3m2 + 30m4 + 30m6 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m2'. 3m2(1 + 10m2 + 10m4) = 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 '(1 + 10m2 + 10m4)' equal to zero and attempt to solve: Simplifying 1 + 10m2 + 10m4 = 0 Solving 1 + 10m2 + 10m4 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + m2 + m4 = 0.0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + m2 + -0.1 + m4 = 0.0 + -0.1 Reorder the terms: 0.1 + -0.1 + m2 + m4 = 0.0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + m2 + m4 = 0.0 + -0.1 m2 + m4 = 0.0 + -0.1 Combine like terms: 0.0 + -0.1 = -0.1 m2 + m4 = -0.1 The m term is m2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m4 = -0.1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m4 = -0.1 + 0.25 Combine like terms: -0.1 + 0.25 = 0.15 1.25 + m4 = 0.15 Factor a perfect square on the left side: (m2 + 0.5)(m2 + 0.5) = 0.15 Calculate the square root of the right side: 0.387298335 Break this problem into two subproblems by setting (m2 + 0.5) equal to 0.387298335 and -0.387298335.Subproblem 1
m2 + 0.5 = 0.387298335 Simplifying m2 + 0.5 = 0.387298335 Reorder the terms: 0.5 + m2 = 0.387298335 Solving 0.5 + m2 = 0.387298335 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m2 = 0.387298335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m2 = 0.387298335 + -0.5 m2 = 0.387298335 + -0.5 Combine like terms: 0.387298335 + -0.5 = -0.112701665 m2 = -0.112701665 Simplifying m2 = -0.112701665 Reorder the terms: 0.112701665 + m2 = -0.112701665 + 0.112701665 Combine like terms: -0.112701665 + 0.112701665 = 0.000000000 0.112701665 + m2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
m2 + 0.5 = -0.387298335 Simplifying m2 + 0.5 = -0.387298335 Reorder the terms: 0.5 + m2 = -0.387298335 Solving 0.5 + m2 = -0.387298335 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m2 = -0.387298335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m2 = -0.387298335 + -0.5 m2 = -0.387298335 + -0.5 Combine like terms: -0.387298335 + -0.5 = -0.887298335 m2 = -0.887298335 Simplifying m2 = -0.887298335 Reorder the terms: 0.887298335 + m2 = -0.887298335 + 0.887298335 Combine like terms: -0.887298335 + 0.887298335 = 0.000000000 0.887298335 + 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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