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Simplifying -9m(2m2 + 6m + -1) = 0 Reorder the terms: -9m(-1 + 6m + 2m2) = 0 (-1 * -9m + 6m * -9m + 2m2 * -9m) = 0 (9m + -54m2 + -18m3) = 0 Solving 9m + -54m2 + -18m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '9m'. 9m(1 + -6m + -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 '(1 + -6m + -2m2)' equal to zero and attempt to solve: Simplifying 1 + -6m + -2m2 = 0 Solving 1 + -6m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 3m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 3m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 3m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 3m + m2 = 0 + 0.5 3m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 3m + m2 = 0.5 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 0.5 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + 3m + m2 = 2.75 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (m + 1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
m + 1.5 = 1.658312395 Simplifying m + 1.5 = 1.658312395 Reorder the terms: 1.5 + m = 1.658312395 Solving 1.5 + m = 1.658312395 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 1.658312395 + -1.5 m = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 m = 0.158312395 Simplifying m = 0.158312395Subproblem 2
m + 1.5 = -1.658312395 Simplifying m + 1.5 = -1.658312395 Reorder the terms: 1.5 + m = -1.658312395 Solving 1.5 + m = -1.658312395 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -1.658312395 + -1.5 m = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 m = -3.158312395 Simplifying m = -3.158312395Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.158312395, -3.158312395}Solution
m = {0, 0.158312395, -3.158312395}
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