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Simplifying (m2 + 3m + -6) + (m2 + -2m + 4) = 0 Reorder the terms: (-6 + 3m + m2) + (m2 + -2m + 4) = 0 Remove parenthesis around (-6 + 3m + m2) -6 + 3m + m2 + (m2 + -2m + 4) = 0 Reorder the terms: -6 + 3m + m2 + (4 + -2m + m2) = 0 Remove parenthesis around (4 + -2m + m2) -6 + 3m + m2 + 4 + -2m + m2 = 0 Reorder the terms: -6 + 4 + 3m + -2m + m2 + m2 = 0 Combine like terms: -6 + 4 = -2 -2 + 3m + -2m + m2 + m2 = 0 Combine like terms: 3m + -2m = 1m -2 + 1m + m2 + m2 = 0 Combine like terms: m2 + m2 = 2m2 -2 + 1m + 2m2 = 0 Solving -2 + 1m + 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'. -1 + 0.5m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5m + m2 = 0 + 1 0.5m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5m + m2 = 1 The m term is 0.5m. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5m + 0.0625 + m2 = 1 + 0.0625 Reorder the terms: 0.0625 + 0.5m + m2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + 0.5m + m2 = 1.0625 Factor a perfect square on the left side: (m + 0.25)(m + 0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (m + 0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
m + 0.25 = 1.030776406 Simplifying m + 0.25 = 1.030776406 Reorder the terms: 0.25 + m = 1.030776406 Solving 0.25 + m = 1.030776406 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = 1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = 1.030776406 + -0.25 m = 1.030776406 + -0.25 Combine like terms: 1.030776406 + -0.25 = 0.780776406 m = 0.780776406 Simplifying m = 0.780776406Subproblem 2
m + 0.25 = -1.030776406 Simplifying m + 0.25 = -1.030776406 Reorder the terms: 0.25 + m = -1.030776406 Solving 0.25 + m = -1.030776406 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = -1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = -1.030776406 + -0.25 m = -1.030776406 + -0.25 Combine like terms: -1.030776406 + -0.25 = -1.280776406 m = -1.280776406 Simplifying m = -1.280776406Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.780776406, -1.280776406}
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