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Simplifying 2m3 + -11m2 + 2m = 0 Reorder the terms: 2m + -11m2 + 2m3 = 0 Solving 2m + -11m2 + 2m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(2 + -11m + 2m2) = 0Subproblem 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 '(2 + -11m + 2m2)' equal to zero and attempt to solve: Simplifying 2 + -11m + 2m2 = 0 Solving 2 + -11m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -5.5m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.5m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -5.5m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.5m + m2 = 0 + -1 -5.5m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.5m + m2 = -1 The m term is -5.5m. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5m + 7.5625 + m2 = -1 + 7.5625 Reorder the terms: 7.5625 + -5.5m + m2 = -1 + 7.5625 Combine like terms: -1 + 7.5625 = 6.5625 7.5625 + -5.5m + m2 = 6.5625 Factor a perfect square on the left side: (m + -2.75)(m + -2.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (m + -2.75) equal to 2.561737691 and -2.561737691.Subproblem 1
m + -2.75 = 2.561737691 Simplifying m + -2.75 = 2.561737691 Reorder the terms: -2.75 + m = 2.561737691 Solving -2.75 + m = 2.561737691 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = 2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = 2.561737691 + 2.75 m = 2.561737691 + 2.75 Combine like terms: 2.561737691 + 2.75 = 5.311737691 m = 5.311737691 Simplifying m = 5.311737691Subproblem 2
m + -2.75 = -2.561737691 Simplifying m + -2.75 = -2.561737691 Reorder the terms: -2.75 + m = -2.561737691 Solving -2.75 + m = -2.561737691 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = -2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = -2.561737691 + 2.75 m = -2.561737691 + 2.75 Combine like terms: -2.561737691 + 2.75 = 0.188262309 m = 0.188262309 Simplifying m = 0.188262309Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.311737691, 0.188262309}Solution
m = {0, 5.311737691, 0.188262309}
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