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Simplifying 2m2 + 6m + -9 = 0 Reorder the terms: -9 + 6m + 2m2 = 0 Solving -9 + 6m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 3m + m2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 3m + 4.5 + m2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 3m + m2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 3m + m2 = 0 + 4.5 3m + m2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 3m + m2 = 4.5 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 = 4.5 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 4.5 + 2.25 Combine like terms: 4.5 + 2.25 = 6.75 2.25 + 3m + m2 = 6.75 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (m + 1.5) equal to 2.598076211 and -2.598076211.Subproblem 1
m + 1.5 = 2.598076211 Simplifying m + 1.5 = 2.598076211 Reorder the terms: 1.5 + m = 2.598076211 Solving 1.5 + m = 2.598076211 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 = 2.598076211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 2.598076211 + -1.5 m = 2.598076211 + -1.5 Combine like terms: 2.598076211 + -1.5 = 1.098076211 m = 1.098076211 Simplifying m = 1.098076211Subproblem 2
m + 1.5 = -2.598076211 Simplifying m + 1.5 = -2.598076211 Reorder the terms: 1.5 + m = -2.598076211 Solving 1.5 + m = -2.598076211 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 = -2.598076211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -2.598076211 + -1.5 m = -2.598076211 + -1.5 Combine like terms: -2.598076211 + -1.5 = -4.098076211 m = -4.098076211 Simplifying m = -4.098076211Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.098076211, -4.098076211}
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