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Simplifying 3m(m2 + 2m + -18) = 0 Reorder the terms: 3m(-18 + 2m + m2) = 0 (-18 * 3m + 2m * 3m + m2 * 3m) = 0 (-54m + 6m2 + 3m3) = 0 Solving -54m + 6m2 + 3m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m'. 3m(-18 + 2m + m2) = 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 '(-18 + 2m + m2)' equal to zero and attempt to solve: Simplifying -18 + 2m + m2 = 0 Solving -18 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 2m + 18 + m2 = 0 + 18 Reorder the terms: -18 + 18 + 2m + m2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2m + m2 = 0 + 18 2m + m2 = 0 + 18 Combine like terms: 0 + 18 = 18 2m + m2 = 18 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 18 + 1 Reorder the terms: 1 + 2m + m2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + 2m + m2 = 19 Factor a perfect square on the left side: (m + 1)(m + 1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (m + 1) equal to 4.358898944 and -4.358898944.Subproblem 1
m + 1 = 4.358898944 Simplifying m + 1 = 4.358898944 Reorder the terms: 1 + m = 4.358898944 Solving 1 + m = 4.358898944 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + m = 4.358898944 + -1 m = 4.358898944 + -1 Combine like terms: 4.358898944 + -1 = 3.358898944 m = 3.358898944 Simplifying m = 3.358898944Subproblem 2
m + 1 = -4.358898944 Simplifying m + 1 = -4.358898944 Reorder the terms: 1 + m = -4.358898944 Solving 1 + m = -4.358898944 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -4.358898944 + -1 Combine like terms: 1 + -1 = 0 0 + m = -4.358898944 + -1 m = -4.358898944 + -1 Combine like terms: -4.358898944 + -1 = -5.358898944 m = -5.358898944 Simplifying m = -5.358898944Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.358898944, -5.358898944}Solution
m = {0, 3.358898944, -5.358898944}
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