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Simplifying 2m2 + -11 + -1 = -11m Reorder the terms: -11 + -1 + 2m2 = -11m Combine like terms: -11 + -1 = -12 -12 + 2m2 = -11m Solving -12 + 2m2 = -11m Solving for variable 'm'. Reorder the terms: -12 + 11m + 2m2 = -11m + 11m Combine like terms: -11m + 11m = 0 -12 + 11m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 5.5m + m2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5.5m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + 5.5m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5.5m + m2 = 0 + 6 5.5m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 5.5m + m2 = 6 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 = 6 + 7.5625 Reorder the terms: 7.5625 + 5.5m + m2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + 5.5m + m2 = 13.5625 Factor a perfect square on the left side: (m + 2.75)(m + 2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (m + 2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
m + 2.75 = 3.682729966 Simplifying m + 2.75 = 3.682729966 Reorder the terms: 2.75 + m = 3.682729966 Solving 2.75 + m = 3.682729966 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 = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + m = 3.682729966 + -2.75 m = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 m = 0.932729966 Simplifying m = 0.932729966Subproblem 2
m + 2.75 = -3.682729966 Simplifying m + 2.75 = -3.682729966 Reorder the terms: 2.75 + m = -3.682729966 Solving 2.75 + m = -3.682729966 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 = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + m = -3.682729966 + -2.75 m = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 m = -6.432729966 Simplifying m = -6.432729966Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.932729966, -6.432729966}
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