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Simplifying 3m2 + 228m + -1000 = 0 Reorder the terms: -1000 + 228m + 3m2 = 0 Solving -1000 + 228m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -333.3333333 + 76m + m2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + 76m + 333.3333333 + m2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + 76m + m2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + 76m + m2 = 0 + 333.3333333 76m + m2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 76m + m2 = 333.3333333 The m term is 76m. Take half its coefficient (38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. 76m + 1444 + m2 = 333.3333333 + 1444 Reorder the terms: 1444 + 76m + m2 = 333.3333333 + 1444 Combine like terms: 333.3333333 + 1444 = 1777.3333333 1444 + 76m + m2 = 1777.3333333 Factor a perfect square on the left side: (m + 38)(m + 38) = 1777.3333333 Calculate the square root of the right side: 42.158431343 Break this problem into two subproblems by setting (m + 38) equal to 42.158431343 and -42.158431343.Subproblem 1
m + 38 = 42.158431343 Simplifying m + 38 = 42.158431343 Reorder the terms: 38 + m = 42.158431343 Solving 38 + m = 42.158431343 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + m = 42.158431343 + -38 Combine like terms: 38 + -38 = 0 0 + m = 42.158431343 + -38 m = 42.158431343 + -38 Combine like terms: 42.158431343 + -38 = 4.158431343 m = 4.158431343 Simplifying m = 4.158431343Subproblem 2
m + 38 = -42.158431343 Simplifying m + 38 = -42.158431343 Reorder the terms: 38 + m = -42.158431343 Solving 38 + m = -42.158431343 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + m = -42.158431343 + -38 Combine like terms: 38 + -38 = 0 0 + m = -42.158431343 + -38 m = -42.158431343 + -38 Combine like terms: -42.158431343 + -38 = -80.158431343 m = -80.158431343 Simplifying m = -80.158431343Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.158431343, -80.158431343}
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