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Simplifying 12m2 + -12 = 11m Reorder the terms: -12 + 12m2 = 11m Solving -12 + 12m2 = 11m Solving for variable 'm'. Reorder the terms: -12 + -11m + 12m2 = 11m + -11m Combine like terms: 11m + -11m = 0 -12 + -11m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + -0.9166666667m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.9166666667m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.9166666667m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.9166666667m + m2 = 0 + 1 -0.9166666667m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.9166666667m + m2 = 1 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 = 1 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667m + m2 = 1 + 0.2100694445 Combine like terms: 1 + 0.2100694445 = 1.2100694445 0.2100694445 + -0.9166666667m + m2 = 1.2100694445 Factor a perfect square on the left side: (m + -0.4583333334)(m + -0.4583333334) = 1.2100694445 Calculate the square root of the right side: 1.100031565 Break this problem into two subproblems by setting (m + -0.4583333334) equal to 1.100031565 and -1.100031565.Subproblem 1
m + -0.4583333334 = 1.100031565 Simplifying m + -0.4583333334 = 1.100031565 Reorder the terms: -0.4583333334 + m = 1.100031565 Solving -0.4583333334 + m = 1.100031565 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 = 1.100031565 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + m = 1.100031565 + 0.4583333334 m = 1.100031565 + 0.4583333334 Combine like terms: 1.100031565 + 0.4583333334 = 1.5583648984 m = 1.5583648984 Simplifying m = 1.5583648984Subproblem 2
m + -0.4583333334 = -1.100031565 Simplifying m + -0.4583333334 = -1.100031565 Reorder the terms: -0.4583333334 + m = -1.100031565 Solving -0.4583333334 + m = -1.100031565 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 = -1.100031565 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + m = -1.100031565 + 0.4583333334 m = -1.100031565 + 0.4583333334 Combine like terms: -1.100031565 + 0.4583333334 = -0.6416982316 m = -0.6416982316 Simplifying m = -0.6416982316Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.5583648984, -0.6416982316}
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