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Simplifying -11x2 + 12x + 6 = 0 Reorder the terms: 6 + 12x + -11x2 = 0 Solving 6 + 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'. -0.5454545455 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -1.090909091x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -1.090909091x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -1.090909091x + x2 = 0 + 0.5454545455 -1.090909091x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -1.090909091x + x2 = 0.5454545455 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 = 0.5454545455 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 0.5454545455 + 0.2975206612 Combine like terms: 0.5454545455 + 0.2975206612 = 0.8429752067 0.2975206612 + -1.090909091x + x2 = 0.8429752067 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 0.8429752067 Calculate the square root of the right side: 0.918136813 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 0.918136813 and -0.918136813.Subproblem 1
x + -0.5454545455 = 0.918136813 Simplifying x + -0.5454545455 = 0.918136813 Reorder the terms: -0.5454545455 + x = 0.918136813 Solving -0.5454545455 + x = 0.918136813 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 = 0.918136813 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 0.918136813 + 0.5454545455 x = 0.918136813 + 0.5454545455 Combine like terms: 0.918136813 + 0.5454545455 = 1.4635913585 x = 1.4635913585 Simplifying x = 1.4635913585Subproblem 2
x + -0.5454545455 = -0.918136813 Simplifying x + -0.5454545455 = -0.918136813 Reorder the terms: -0.5454545455 + x = -0.918136813 Solving -0.5454545455 + x = -0.918136813 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 = -0.918136813 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -0.918136813 + 0.5454545455 x = -0.918136813 + 0.5454545455 Combine like terms: -0.918136813 + 0.5454545455 = -0.3726822675 x = -0.3726822675 Simplifying x = -0.3726822675Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4635913585, -0.3726822675}
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