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Simplifying 24m2 + -22m + -3 = 0 Reorder the terms: -3 + -22m + 24m2 = 0 Solving -3 + -22m + 24m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.125 + -0.9166666667m + m2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.9166666667m + 0.125 + m2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.9166666667m + m2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.9166666667m + m2 = 0 + 0.125 -0.9166666667m + m2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.9166666667m + m2 = 0.125 The m term is -0.9166666667m. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667m + 0.2100694445 + m2 = 0.125 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667m + m2 = 0.125 + 0.2100694445 Combine like terms: 0.125 + 0.2100694445 = 0.3350694445 0.2100694445 + -0.9166666667m + m2 = 0.3350694445 Factor a perfect square on the left side: (m + -0.4583333334)(m + -0.4583333334) = 0.3350694445 Calculate the square root of the right side: 0.578851833 Break this problem into two subproblems by setting (m + -0.4583333334) equal to 0.578851833 and -0.578851833.Subproblem 1
m + -0.4583333334 = 0.578851833 Simplifying m + -0.4583333334 = 0.578851833 Reorder the terms: -0.4583333334 + m = 0.578851833 Solving -0.4583333334 + m = 0.578851833 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + m = 0.578851833 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + m = 0.578851833 + 0.4583333334 m = 0.578851833 + 0.4583333334 Combine like terms: 0.578851833 + 0.4583333334 = 1.0371851664 m = 1.0371851664 Simplifying m = 1.0371851664Subproblem 2
m + -0.4583333334 = -0.578851833 Simplifying m + -0.4583333334 = -0.578851833 Reorder the terms: -0.4583333334 + m = -0.578851833 Solving -0.4583333334 + m = -0.578851833 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + m = -0.578851833 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + m = -0.578851833 + 0.4583333334 m = -0.578851833 + 0.4583333334 Combine like terms: -0.578851833 + 0.4583333334 = -0.1205184996 m = -0.1205184996 Simplifying m = -0.1205184996Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.0371851664, -0.1205184996}
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