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Simplifying 11x2 + -4x + -11 = 0 Reorder the terms: -11 + -4x + 11x2 = 0 Solving -11 + -4x + 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'. -1 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.3636363636x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.3636363636x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.3636363636x + x2 = 0 + 1 -0.3636363636x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.3636363636x + x2 = 1 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 1 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 1 + 0.03305785123 Combine like terms: 1 + 0.03305785123 = 1.03305785123 0.03305785123 + -0.3636363636x + x2 = 1.03305785123 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 1.03305785123 Calculate the square root of the right side: 1.016394535 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 1.016394535 and -1.016394535.Subproblem 1
x + -0.1818181818 = 1.016394535 Simplifying x + -0.1818181818 = 1.016394535 Reorder the terms: -0.1818181818 + x = 1.016394535 Solving -0.1818181818 + x = 1.016394535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 1.016394535 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 1.016394535 + 0.1818181818 x = 1.016394535 + 0.1818181818 Combine like terms: 1.016394535 + 0.1818181818 = 1.1982127168 x = 1.1982127168 Simplifying x = 1.1982127168Subproblem 2
x + -0.1818181818 = -1.016394535 Simplifying x + -0.1818181818 = -1.016394535 Reorder the terms: -0.1818181818 + x = -1.016394535 Solving -0.1818181818 + x = -1.016394535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -1.016394535 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -1.016394535 + 0.1818181818 x = -1.016394535 + 0.1818181818 Combine like terms: -1.016394535 + 0.1818181818 = -0.8345763532 x = -0.8345763532 Simplifying x = -0.8345763532Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1982127168, -0.8345763532}
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