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Simplifying 120m9 + -108m7 + -72m5 = 0 Reorder the terms: -72m5 + -108m7 + 120m9 = 0 Solving -72m5 + -108m7 + 120m9 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '12m5'. 12m5(-6 + -9m2 + 10m4) = 0 Ignore the factor 12.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 + -9m2 + 10m4)' equal to zero and attempt to solve: Simplifying -6 + -9m2 + 10m4 = 0 Solving -6 + -9m2 + 10m4 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -0.9m2 + m4 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.9m2 + 0.6 + m4 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.9m2 + m4 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.9m2 + m4 = 0.0 + 0.6 -0.9m2 + m4 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -0.9m2 + m4 = 0.6 The m term is -0.9m2. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9m2 + 0.2025 + m4 = 0.6 + 0.2025 Reorder the terms: 0.2025 + -0.9m2 + m4 = 0.6 + 0.2025 Combine like terms: 0.6 + 0.2025 = 0.8025 0.2025 + -0.9m2 + m4 = 0.8025 Factor a perfect square on the left side: (m2 + -0.45)(m2 + -0.45) = 0.8025 Calculate the square root of the right side: 0.895823643 Break this problem into two subproblems by setting (m2 + -0.45) equal to 0.895823643 and -0.895823643.Subproblem 1
m2 + -0.45 = 0.895823643 Simplifying m2 + -0.45 = 0.895823643 Reorder the terms: -0.45 + m2 = 0.895823643 Solving -0.45 + m2 = 0.895823643 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + m2 = 0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + m2 = 0.895823643 + 0.45 m2 = 0.895823643 + 0.45 Combine like terms: 0.895823643 + 0.45 = 1.345823643 m2 = 1.345823643 Simplifying m2 = 1.345823643 Take the square root of each side: m = {-1.160096394, 1.160096394}Subproblem 2
m2 + -0.45 = -0.895823643 Simplifying m2 + -0.45 = -0.895823643 Reorder the terms: -0.45 + m2 = -0.895823643 Solving -0.45 + m2 = -0.895823643 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + m2 = -0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + m2 = -0.895823643 + 0.45 m2 = -0.895823643 + 0.45 Combine like terms: -0.895823643 + 0.45 = -0.445823643 m2 = -0.445823643 Simplifying m2 = -0.445823643 Reorder the terms: 0.445823643 + m2 = -0.445823643 + 0.445823643 Combine like terms: -0.445823643 + 0.445823643 = 0.000000000 0.445823643 + 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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