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Simplifying 12x2 + -11x = 11 Reorder the terms: -11x + 12x2 = 11 Solving -11x + 12x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -11x + 12x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -0.9166666667x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -0.9166666667x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -0.9166666667x + x2 = 0 + 0.9166666667 -0.9166666667x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -0.9166666667x + x2 = 0.9166666667 The x term is -0.9166666667x. 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. -0.9166666667x + 0.2100694445 + x2 = 0.9166666667 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 0.9166666667 + 0.2100694445 Combine like terms: 0.9166666667 + 0.2100694445 = 1.1267361112 0.2100694445 + -0.9166666667x + x2 = 1.1267361112 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 1.1267361112 Calculate the square root of the right side: 1.061478267 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 1.061478267 and -1.061478267.Subproblem 1
x + -0.4583333334 = 1.061478267 Simplifying x + -0.4583333334 = 1.061478267 Reorder the terms: -0.4583333334 + x = 1.061478267 Solving -0.4583333334 + x = 1.061478267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = 1.061478267 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 1.061478267 + 0.4583333334 x = 1.061478267 + 0.4583333334 Combine like terms: 1.061478267 + 0.4583333334 = 1.5198116004 x = 1.5198116004 Simplifying x = 1.5198116004Subproblem 2
x + -0.4583333334 = -1.061478267 Simplifying x + -0.4583333334 = -1.061478267 Reorder the terms: -0.4583333334 + x = -1.061478267 Solving -0.4583333334 + x = -1.061478267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = -1.061478267 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -1.061478267 + 0.4583333334 x = -1.061478267 + 0.4583333334 Combine like terms: -1.061478267 + 0.4583333334 = -0.6031449336 x = -0.6031449336 Simplifying x = -0.6031449336Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5198116004, -0.6031449336}
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