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Simplifying 6m2 + -9m + -11 = 0 Reorder the terms: -11 + -9m + 6m2 = 0 Solving -11 + -9m + 6m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -1.5m + m2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -1.5m + 1.833333333 + m2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -1.5m + m2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -1.5m + m2 = 0 + 1.833333333 -1.5m + m2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -1.5m + m2 = 1.833333333 The m term is -1.5m. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5m + 0.5625 + m2 = 1.833333333 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 1.833333333 + 0.5625 Combine like terms: 1.833333333 + 0.5625 = 2.395833333 0.5625 + -1.5m + m2 = 2.395833333 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 2.395833333 Calculate the square root of the right side: 1.547847968 Break this problem into two subproblems by setting (m + -0.75) equal to 1.547847968 and -1.547847968.Subproblem 1
m + -0.75 = 1.547847968 Simplifying m + -0.75 = 1.547847968 Reorder the terms: -0.75 + m = 1.547847968 Solving -0.75 + m = 1.547847968 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 1.547847968 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 1.547847968 + 0.75 m = 1.547847968 + 0.75 Combine like terms: 1.547847968 + 0.75 = 2.297847968 m = 2.297847968 Simplifying m = 2.297847968Subproblem 2
m + -0.75 = -1.547847968 Simplifying m + -0.75 = -1.547847968 Reorder the terms: -0.75 + m = -1.547847968 Solving -0.75 + m = -1.547847968 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -1.547847968 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -1.547847968 + 0.75 m = -1.547847968 + 0.75 Combine like terms: -1.547847968 + 0.75 = -0.797847968 m = -0.797847968 Simplifying m = -0.797847968Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.297847968, -0.797847968}
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