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Simplifying 11x2 + -12x + 3 = 0 Reorder the terms: 3 + -12x + 11x2 = 0 Solving 3 + -12x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.2727272727 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + -1.090909091x + -0.2727272727 + x2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + -1.090909091x + x2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + -1.090909091x + x2 = 0 + -0.2727272727 -1.090909091x + x2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 -1.090909091x + x2 = -0.2727272727 The x term is -1.090909091x. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091x + 0.2975206612 + x2 = -0.2727272727 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = -0.2727272727 + 0.2975206612 Combine like terms: -0.2727272727 + 0.2975206612 = 0.0247933885 0.2975206612 + -1.090909091x + x2 = 0.0247933885 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 0.0247933885 Calculate the square root of the right side: 0.157459165 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 0.157459165 and -0.157459165.Subproblem 1
x + -0.5454545455 = 0.157459165 Simplifying x + -0.5454545455 = 0.157459165 Reorder the terms: -0.5454545455 + x = 0.157459165 Solving -0.5454545455 + x = 0.157459165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = 0.157459165 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 0.157459165 + 0.5454545455 x = 0.157459165 + 0.5454545455 Combine like terms: 0.157459165 + 0.5454545455 = 0.7029137105 x = 0.7029137105 Simplifying x = 0.7029137105Subproblem 2
x + -0.5454545455 = -0.157459165 Simplifying x + -0.5454545455 = -0.157459165 Reorder the terms: -0.5454545455 + x = -0.157459165 Solving -0.5454545455 + x = -0.157459165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = -0.157459165 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -0.157459165 + 0.5454545455 x = -0.157459165 + 0.5454545455 Combine like terms: -0.157459165 + 0.5454545455 = 0.3879953805 x = 0.3879953805 Simplifying x = 0.3879953805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7029137105, 0.3879953805}
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