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Simplifying m7 + 18m5 + 8m3 = 0 Reorder the terms: 8m3 + 18m5 + m7 = 0 Solving 8m3 + 18m5 + m7 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm3'. m3(8 + 18m2 + m4) = 0Subproblem 1
Set the factor 'm3' equal to zero and attempt to solve: Simplifying m3 = 0 Solving m3 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m3 = 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 '(8 + 18m2 + m4)' equal to zero and attempt to solve: Simplifying 8 + 18m2 + m4 = 0 Solving 8 + 18m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 18m2 + -8 + m4 = 0 + -8 Reorder the terms: 8 + -8 + 18m2 + m4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 18m2 + m4 = 0 + -8 18m2 + m4 = 0 + -8 Combine like terms: 0 + -8 = -8 18m2 + m4 = -8 The m term is 18m2. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18m2 + 81 + m4 = -8 + 81 Reorder the terms: 81 + 18m2 + m4 = -8 + 81 Combine like terms: -8 + 81 = 73 81 + 18m2 + m4 = 73 Factor a perfect square on the left side: (m2 + 9)(m2 + 9) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (m2 + 9) equal to 8.544003745 and -8.544003745.Subproblem 1
m2 + 9 = 8.544003745 Simplifying m2 + 9 = 8.544003745 Reorder the terms: 9 + m2 = 8.544003745 Solving 9 + m2 = 8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m2 = 8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + m2 = 8.544003745 + -9 m2 = 8.544003745 + -9 Combine like terms: 8.544003745 + -9 = -0.455996255 m2 = -0.455996255 Simplifying m2 = -0.455996255 Reorder the terms: 0.455996255 + m2 = -0.455996255 + 0.455996255 Combine like terms: -0.455996255 + 0.455996255 = 0.000000000 0.455996255 + 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 + 9 = -8.544003745 Simplifying m2 + 9 = -8.544003745 Reorder the terms: 9 + m2 = -8.544003745 Solving 9 + m2 = -8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m2 = -8.544003745 + -9 Combine like terms: 9 + -9 = 0 0 + m2 = -8.544003745 + -9 m2 = -8.544003745 + -9 Combine like terms: -8.544003745 + -9 = -17.544003745 m2 = -17.544003745 Simplifying m2 = -17.544003745 Reorder the terms: 17.544003745 + m2 = -17.544003745 + 17.544003745 Combine like terms: -17.544003745 + 17.544003745 = 0.000000000 17.544003745 + 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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