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Simplifying 3m5 + -30m3 = 63m Reorder the terms: -30m3 + 3m5 = 63m Solving -30m3 + 3m5 = 63m Solving for variable 'm'. Reorder the terms: -63m + -30m3 + 3m5 = 63m + -63m Combine like terms: 63m + -63m = 0 -63m + -30m3 + 3m5 = 0 Factor out the Greatest Common Factor (GCF), '3m'. 3m(-21 + -10m2 + m4) = 0 Ignore the factor 3.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 '(-21 + -10m2 + m4)' equal to zero and attempt to solve: Simplifying -21 + -10m2 + m4 = 0 Solving -21 + -10m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -10m2 + 21 + m4 = 0 + 21 Reorder the terms: -21 + 21 + -10m2 + m4 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -10m2 + m4 = 0 + 21 -10m2 + m4 = 0 + 21 Combine like terms: 0 + 21 = 21 -10m2 + m4 = 21 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 = 21 + 25 Reorder the terms: 25 + -10m2 + m4 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + -10m2 + m4 = 46 Factor a perfect square on the left side: (m2 + -5)(m2 + -5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (m2 + -5) equal to 6.782329983 and -6.782329983.Subproblem 1
m2 + -5 = 6.782329983 Simplifying m2 + -5 = 6.782329983 Reorder the terms: -5 + m2 = 6.782329983 Solving -5 + m2 = 6.782329983 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 = 6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + m2 = 6.782329983 + 5 m2 = 6.782329983 + 5 Combine like terms: 6.782329983 + 5 = 11.782329983 m2 = 11.782329983 Simplifying m2 = 11.782329983 Take the square root of each side: m = {-3.432539873, 3.432539873}Subproblem 2
m2 + -5 = -6.782329983 Simplifying m2 + -5 = -6.782329983 Reorder the terms: -5 + m2 = -6.782329983 Solving -5 + m2 = -6.782329983 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 = -6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + m2 = -6.782329983 + 5 m2 = -6.782329983 + 5 Combine like terms: -6.782329983 + 5 = -1.782329983 m2 = -1.782329983 Simplifying m2 = -1.782329983 Reorder the terms: 1.782329983 + m2 = -1.782329983 + 1.782329983 Combine like terms: -1.782329983 + 1.782329983 = 0.000000000 1.782329983 + 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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