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Simplifying 3m(m + -6) = 6 Reorder the terms: 3m(-6 + m) = 6 (-6 * 3m + m * 3m) = 6 (-18m + 3m2) = 6 Solving -18m + 3m2 = 6 Solving for variable 'm'. Reorder the terms: -6 + -18m + 3m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -18m + 3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -6m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -6m + m2)' equal to zero and attempt to solve: Simplifying -2 + -6m + m2 = 0 Solving -2 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -6m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -6m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6m + m2 = 0 + 2 -6m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6m + m2 = 2 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 = 2 + 9 Reorder the terms: 9 + -6m + m2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6m + m2 = 11 Factor a perfect square on the left side: (m + -3)(m + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -3) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -3 = 3.31662479 Simplifying m + -3 = 3.31662479 Reorder the terms: -3 + m = 3.31662479 Solving -3 + m = 3.31662479 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 = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.31662479 + 3 m = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 m = 6.31662479 Simplifying m = 6.31662479Subproblem 2
m + -3 = -3.31662479 Simplifying m + -3 = -3.31662479 Reorder the terms: -3 + m = -3.31662479 Solving -3 + m = -3.31662479 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 = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.31662479 + 3 m = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 m = -0.31662479 Simplifying m = -0.31662479Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.31662479, -0.31662479}Solution
m = {6.31662479, -0.31662479}
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