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Simplifying 6m9 + -9m7 + -18m5 = 0 Reorder the terms: -18m5 + -9m7 + 6m9 = 0 Solving -18m5 + -9m7 + 6m9 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m5'. 3m5(-6 + -3m2 + 2m4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'm5' equal to zero and attempt to solve: Simplifying m5 = 0 Solving m5 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-6 + -3m2 + 2m4)' equal to zero and attempt to solve: Simplifying -6 + -3m2 + 2m4 = 0 Solving -6 + -3m2 + 2m4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -1.5m2 + m4 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.5m2 + 3 + m4 = 0 + 3 Reorder the terms: -3 + 3 + -1.5m2 + m4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.5m2 + m4 = 0 + 3 -1.5m2 + m4 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.5m2 + m4 = 3 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 = 3 + 0.5625 Reorder the terms: 0.5625 + -1.5m2 + m4 = 3 + 0.5625 Combine like terms: 3 + 0.5625 = 3.5625 0.5625 + -1.5m2 + m4 = 3.5625 Factor a perfect square on the left side: (m2 + -0.75)(m2 + -0.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (m2 + -0.75) equal to 1.887458609 and -1.887458609.Subproblem 1
m2 + -0.75 = 1.887458609 Simplifying m2 + -0.75 = 1.887458609 Reorder the terms: -0.75 + m2 = 1.887458609 Solving -0.75 + m2 = 1.887458609 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 = 1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m2 = 1.887458609 + 0.75 m2 = 1.887458609 + 0.75 Combine like terms: 1.887458609 + 0.75 = 2.637458609 m2 = 2.637458609 Simplifying m2 = 2.637458609 Take the square root of each side: m = {-1.624025434, 1.624025434}Subproblem 2
m2 + -0.75 = -1.887458609 Simplifying m2 + -0.75 = -1.887458609 Reorder the terms: -0.75 + m2 = -1.887458609 Solving -0.75 + m2 = -1.887458609 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 = -1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m2 = -1.887458609 + 0.75 m2 = -1.887458609 + 0.75 Combine like terms: -1.887458609 + 0.75 = -1.137458609 m2 = -1.137458609 Simplifying m2 = -1.137458609 Reorder the terms: 1.137458609 + m2 = -1.137458609 + 1.137458609 Combine like terms: -1.137458609 + 1.137458609 = 0.000000000 1.137458609 + 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. The solution to this equation could not be determined.
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