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Simplifying 11x2 + -12x + -32 = 0 Reorder the terms: -32 + -12x + 11x2 = 0 Solving -32 + -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'. -2.909090909 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '2.909090909' to each side of the equation. -2.909090909 + -1.090909091x + 2.909090909 + x2 = 0 + 2.909090909 Reorder the terms: -2.909090909 + 2.909090909 + -1.090909091x + x2 = 0 + 2.909090909 Combine like terms: -2.909090909 + 2.909090909 = 0.000000000 0.000000000 + -1.090909091x + x2 = 0 + 2.909090909 -1.090909091x + x2 = 0 + 2.909090909 Combine like terms: 0 + 2.909090909 = 2.909090909 -1.090909091x + x2 = 2.909090909 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 = 2.909090909 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 2.909090909 + 0.2975206612 Combine like terms: 2.909090909 + 0.2975206612 = 3.2066115702 0.2975206612 + -1.090909091x + x2 = 3.2066115702 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 3.2066115702 Calculate the square root of the right side: 1.790701418 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 1.790701418 and -1.790701418.Subproblem 1
x + -0.5454545455 = 1.790701418 Simplifying x + -0.5454545455 = 1.790701418 Reorder the terms: -0.5454545455 + x = 1.790701418 Solving -0.5454545455 + x = 1.790701418 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 = 1.790701418 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 1.790701418 + 0.5454545455 x = 1.790701418 + 0.5454545455 Combine like terms: 1.790701418 + 0.5454545455 = 2.3361559635 x = 2.3361559635 Simplifying x = 2.3361559635Subproblem 2
x + -0.5454545455 = -1.790701418 Simplifying x + -0.5454545455 = -1.790701418 Reorder the terms: -0.5454545455 + x = -1.790701418 Solving -0.5454545455 + x = -1.790701418 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 = -1.790701418 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -1.790701418 + 0.5454545455 x = -1.790701418 + 0.5454545455 Combine like terms: -1.790701418 + 0.5454545455 = -1.2452468725 x = -1.2452468725 Simplifying x = -1.2452468725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3361559635, -1.2452468725}
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