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Simplifying 11x2 + -1x + -11 = 0 Reorder the terms: -11 + -1x + 11x2 = 0 Solving -11 + -1x + 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 + -0.09090909091x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.09090909091x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.09090909091x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.09090909091x + x2 = 0 + 1 -0.09090909091x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.09090909091x + x2 = 1 The x term is -0.09090909091x. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091x + 0.002066115703 + x2 = 1 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091x + x2 = 1 + 0.002066115703 Combine like terms: 1 + 0.002066115703 = 1.002066115703 0.002066115703 + -0.09090909091x + x2 = 1.002066115703 Factor a perfect square on the left side: (x + -0.04545454546)(x + -0.04545454546) = 1.002066115703 Calculate the square root of the right side: 1.001032525 Break this problem into two subproblems by setting (x + -0.04545454546) equal to 1.001032525 and -1.001032525.Subproblem 1
x + -0.04545454546 = 1.001032525 Simplifying x + -0.04545454546 = 1.001032525 Reorder the terms: -0.04545454546 + x = 1.001032525 Solving -0.04545454546 + x = 1.001032525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = 1.001032525 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = 1.001032525 + 0.04545454546 x = 1.001032525 + 0.04545454546 Combine like terms: 1.001032525 + 0.04545454546 = 1.04648707046 x = 1.04648707046 Simplifying x = 1.04648707046Subproblem 2
x + -0.04545454546 = -1.001032525 Simplifying x + -0.04545454546 = -1.001032525 Reorder the terms: -0.04545454546 + x = -1.001032525 Solving -0.04545454546 + x = -1.001032525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + x = -1.001032525 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = -1.001032525 + 0.04545454546 x = -1.001032525 + 0.04545454546 Combine like terms: -1.001032525 + 0.04545454546 = -0.95557797954 x = -0.95557797954 Simplifying x = -0.95557797954Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.04648707046, -0.95557797954}
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