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Simplifying 15m9 + -24m7 + -21m5 = 0 Reorder the terms: -21m5 + -24m7 + 15m9 = 0 Solving -21m5 + -24m7 + 15m9 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m5'. 3m5(-7 + -8m2 + 5m4) = 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 '(-7 + -8m2 + 5m4)' equal to zero and attempt to solve: Simplifying -7 + -8m2 + 5m4 = 0 Solving -7 + -8m2 + 5m4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1.6m2 + m4 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.6m2 + 1.4 + m4 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.6m2 + m4 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.6m2 + m4 = 0 + 1.4 -1.6m2 + m4 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.6m2 + m4 = 1.4 The m term is -1.6m2. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6m2 + 0.64 + m4 = 1.4 + 0.64 Reorder the terms: 0.64 + -1.6m2 + m4 = 1.4 + 0.64 Combine like terms: 1.4 + 0.64 = 2.04 0.64 + -1.6m2 + m4 = 2.04 Factor a perfect square on the left side: (m2 + -0.8)(m2 + -0.8) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (m2 + -0.8) equal to 1.428285686 and -1.428285686.Subproblem 1
m2 + -0.8 = 1.428285686 Simplifying m2 + -0.8 = 1.428285686 Reorder the terms: -0.8 + m2 = 1.428285686 Solving -0.8 + m2 = 1.428285686 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + m2 = 1.428285686 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + m2 = 1.428285686 + 0.8 m2 = 1.428285686 + 0.8 Combine like terms: 1.428285686 + 0.8 = 2.228285686 m2 = 2.228285686 Simplifying m2 = 2.228285686 Take the square root of each side: m = {-1.492744347, 1.492744347}Subproblem 2
m2 + -0.8 = -1.428285686 Simplifying m2 + -0.8 = -1.428285686 Reorder the terms: -0.8 + m2 = -1.428285686 Solving -0.8 + m2 = -1.428285686 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + m2 = -1.428285686 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + m2 = -1.428285686 + 0.8 m2 = -1.428285686 + 0.8 Combine like terms: -1.428285686 + 0.8 = -0.628285686 m2 = -0.628285686 Simplifying m2 = -0.628285686 Reorder the terms: 0.628285686 + m2 = -0.628285686 + 0.628285686 Combine like terms: -0.628285686 + 0.628285686 = 0.000000000 0.628285686 + 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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