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Simplifying 18m3 + 9m2 + -45m = 0 Reorder the terms: -45m + 9m2 + 18m3 = 0 Solving -45m + 9m2 + 18m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '9m'. 9m(-5 + m + 2m2) = 0 Ignore the factor 9.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 '(-5 + m + 2m2)' equal to zero and attempt to solve: Simplifying -5 + m + 2m2 = 0 Solving -5 + m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 0.5m + m2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5m + 2.5 + m2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5m + m2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5m + m2 = 0 + 2.5 0.5m + m2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5m + m2 = 2.5 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5m + 0.25 + m2 = 2.5 + 0.25 Reorder the terms: 0.25 + 0.5m + m2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + 0.5m + m2 = 2.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (m + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
m + 0.5 = 1.658312395 Simplifying m + 0.5 = 1.658312395 Reorder the terms: 0.5 + m = 1.658312395 Solving 0.5 + m = 1.658312395 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.658312395 + -0.5 m = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 m = 1.158312395 Simplifying m = 1.158312395Subproblem 2
m + 0.5 = -1.658312395 Simplifying m + 0.5 = -1.658312395 Reorder the terms: 0.5 + m = -1.658312395 Solving 0.5 + m = -1.658312395 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.658312395 + -0.5 m = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 m = -2.158312395 Simplifying m = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.158312395, -2.158312395}Solution
m = {0, 1.158312395, -2.158312395}
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