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Simplifying 11m2 + -11m + -1 = 9m2 Reorder the terms: -1 + -11m + 11m2 = 9m2 Solving -1 + -11m + 11m2 = 9m2 Solving for variable 'm'. Combine like terms: 11m2 + -9m2 = 2m2 -1 + -11m + 2m2 = 9m2 + -9m2 Combine like terms: 9m2 + -9m2 = 0 -1 + -11m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -5.5m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.5m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.5m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.5m + m2 = 0 + 0.5 -5.5m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.5m + m2 = 0.5 The m term is -5.5m. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5m + 7.5625 + m2 = 0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5m + m2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + -5.5m + m2 = 8.0625 Factor a perfect square on the left side: (m + -2.75)(m + -2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (m + -2.75) equal to 2.839454173 and -2.839454173.Subproblem 1
m + -2.75 = 2.839454173 Simplifying m + -2.75 = 2.839454173 Reorder the terms: -2.75 + m = 2.839454173 Solving -2.75 + m = 2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = 2.839454173 + 2.75 m = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 m = 5.589454173 Simplifying m = 5.589454173Subproblem 2
m + -2.75 = -2.839454173 Simplifying m + -2.75 = -2.839454173 Reorder the terms: -2.75 + m = -2.839454173 Solving -2.75 + m = -2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + m = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + m = -2.839454173 + 2.75 m = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 m = -0.089454173 Simplifying m = -0.089454173Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.589454173, -0.089454173}
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