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Simplifying -54m3 + 60m2 + 36m = 0 Reorder the terms: 36m + 60m2 + -54m3 = 0 Solving 36m + 60m2 + -54m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '6m'. 6m(6 + 10m + -9m2) = 0 Ignore the factor 6.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 '(6 + 10m + -9m2)' equal to zero and attempt to solve: Simplifying 6 + 10m + -9m2 = 0 Solving 6 + 10m + -9m2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.6666666667 + -1.111111111m + m2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.111111111m + 0.6666666667 + m2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.111111111m + m2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.111111111m + m2 = 0 + 0.6666666667 -1.111111111m + m2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.111111111m + m2 = 0.6666666667 The m term is -1.111111111m. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111m + 0.3086419752 + m2 = 0.6666666667 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111m + m2 = 0.6666666667 + 0.3086419752 Combine like terms: 0.6666666667 + 0.3086419752 = 0.9753086419 0.3086419752 + -1.111111111m + m2 = 0.9753086419 Factor a perfect square on the left side: (m + -0.5555555555)(m + -0.5555555555) = 0.9753086419 Calculate the square root of the right side: 0.987577157 Break this problem into two subproblems by setting (m + -0.5555555555) equal to 0.987577157 and -0.987577157.Subproblem 1
m + -0.5555555555 = 0.987577157 Simplifying m + -0.5555555555 = 0.987577157 Reorder the terms: -0.5555555555 + m = 0.987577157 Solving -0.5555555555 + m = 0.987577157 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + m = 0.987577157 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + m = 0.987577157 + 0.5555555555 m = 0.987577157 + 0.5555555555 Combine like terms: 0.987577157 + 0.5555555555 = 1.5431327125 m = 1.5431327125 Simplifying m = 1.5431327125Subproblem 2
m + -0.5555555555 = -0.987577157 Simplifying m + -0.5555555555 = -0.987577157 Reorder the terms: -0.5555555555 + m = -0.987577157 Solving -0.5555555555 + m = -0.987577157 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + m = -0.987577157 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + m = -0.987577157 + 0.5555555555 m = -0.987577157 + 0.5555555555 Combine like terms: -0.987577157 + 0.5555555555 = -0.4320216015 m = -0.4320216015 Simplifying m = -0.4320216015Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.5431327125, -0.4320216015}Solution
m = {0, 1.5431327125, -0.4320216015}
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