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Simplifying 9m3 + -45m2 + -48m = 0 Reorder the terms: -48m + -45m2 + 9m3 = 0 Solving -48m + -45m2 + 9m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m'. 3m(-16 + -15m + 3m2) = 0 Ignore the factor 3.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 '(-16 + -15m + 3m2)' equal to zero and attempt to solve: Simplifying -16 + -15m + 3m2 = 0 Solving -16 + -15m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -5m + m2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -5m + 5.333333333 + m2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -5m + m2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -5m + m2 = 0 + 5.333333333 -5m + m2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -5m + m2 = 5.333333333 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 5.333333333 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 5.333333333 + 6.25 Combine like terms: 5.333333333 + 6.25 = 11.583333333 6.25 + -5m + m2 = 11.583333333 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 11.583333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (m + -2.5) equal to 3.403429643 and -3.403429643.Subproblem 1
m + -2.5 = 3.403429643 Simplifying m + -2.5 = 3.403429643 Reorder the terms: -2.5 + m = 3.403429643 Solving -2.5 + m = 3.403429643 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 3.403429643 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.403429643 + 2.5 m = 3.403429643 + 2.5 Combine like terms: 3.403429643 + 2.5 = 5.903429643 m = 5.903429643 Simplifying m = 5.903429643Subproblem 2
m + -2.5 = -3.403429643 Simplifying m + -2.5 = -3.403429643 Reorder the terms: -2.5 + m = -3.403429643 Solving -2.5 + m = -3.403429643 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -3.403429643 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.403429643 + 2.5 m = -3.403429643 + 2.5 Combine like terms: -3.403429643 + 2.5 = -0.903429643 m = -0.903429643 Simplifying m = -0.903429643Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.903429643, -0.903429643}Solution
m = {0, 5.903429643, -0.903429643}
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