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Simplifying 2m3 + -12m2 = 50m Reorder the terms: -12m2 + 2m3 = 50m Solving -12m2 + 2m3 = 50m Solving for variable 'm'. Reorder the terms: -50m + -12m2 + 2m3 = 50m + -50m Combine like terms: 50m + -50m = 0 -50m + -12m2 + 2m3 = 0 Factor out the Greatest Common Factor (GCF), '2m'. 2m(-25 + -6m + m2) = 0 Ignore the factor 2.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 '(-25 + -6m + m2)' equal to zero and attempt to solve: Simplifying -25 + -6m + m2 = 0 Solving -25 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -6m + 25 + m2 = 0 + 25 Reorder the terms: -25 + 25 + -6m + m2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6m + m2 = 0 + 25 -6m + m2 = 0 + 25 Combine like terms: 0 + 25 = 25 -6m + m2 = 25 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = 25 + 9 Reorder the terms: 9 + -6m + m2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + -6m + m2 = 34 Factor a perfect square on the left side: (m + -3)(m + -3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (m + -3) equal to 5.830951895 and -5.830951895.Subproblem 1
m + -3 = 5.830951895 Simplifying m + -3 = 5.830951895 Reorder the terms: -3 + m = 5.830951895 Solving -3 + m = 5.830951895 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + m = 5.830951895 + 3 m = 5.830951895 + 3 Combine like terms: 5.830951895 + 3 = 8.830951895 m = 8.830951895 Simplifying m = 8.830951895Subproblem 2
m + -3 = -5.830951895 Simplifying m + -3 = -5.830951895 Reorder the terms: -3 + m = -5.830951895 Solving -3 + m = -5.830951895 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + m = -5.830951895 + 3 m = -5.830951895 + 3 Combine like terms: -5.830951895 + 3 = -2.830951895 m = -2.830951895 Simplifying m = -2.830951895Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.830951895, -2.830951895}Solution
m = {0, 8.830951895, -2.830951895}
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