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Simplifying 12x2 + -11x + 1 = 0 Reorder the terms: 1 + -11x + 12x2 = 0 Solving 1 + -11x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -0.9166666667x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -0.9166666667x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -0.9166666667x + x2 = 0 + -0.08333333333 -0.9166666667x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -0.9166666667x + x2 = -0.08333333333 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 = -0.08333333333 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = -0.08333333333 + 0.2100694445 Combine like terms: -0.08333333333 + 0.2100694445 = 0.12673611117 0.2100694445 + -0.9166666667x + x2 = 0.12673611117 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 0.12673611117 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 0.356000156 and -0.356000156.Subproblem 1
x + -0.4583333334 = 0.356000156 Simplifying x + -0.4583333334 = 0.356000156 Reorder the terms: -0.4583333334 + x = 0.356000156 Solving -0.4583333334 + x = 0.356000156 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 = 0.356000156 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 0.356000156 + 0.4583333334 x = 0.356000156 + 0.4583333334 Combine like terms: 0.356000156 + 0.4583333334 = 0.8143334894 x = 0.8143334894 Simplifying x = 0.8143334894Subproblem 2
x + -0.4583333334 = -0.356000156 Simplifying x + -0.4583333334 = -0.356000156 Reorder the terms: -0.4583333334 + x = -0.356000156 Solving -0.4583333334 + x = -0.356000156 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 = -0.356000156 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -0.356000156 + 0.4583333334 x = -0.356000156 + 0.4583333334 Combine like terms: -0.356000156 + 0.4583333334 = 0.1023331774 x = 0.1023331774 Simplifying x = 0.1023331774Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8143334894, 0.1023331774}
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