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Simplifying 11x2 + -1x = 3 Reorder the terms: -1x + 11x2 = 3 Solving -1x + 11x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -1x + 11x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -1x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.09090909091x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.09090909091x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.09090909091x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.09090909091x + x2 = 0 + 0.2727272727 -0.09090909091x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.09090909091x + x2 = 0.2727272727 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 = 0.2727272727 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091x + x2 = 0.2727272727 + 0.002066115703 Combine like terms: 0.2727272727 + 0.002066115703 = 0.274793388403 0.002066115703 + -0.09090909091x + x2 = 0.274793388403 Factor a perfect square on the left side: (x + -0.04545454546)(x + -0.04545454546) = 0.274793388403 Calculate the square root of the right side: 0.524207391 Break this problem into two subproblems by setting (x + -0.04545454546) equal to 0.524207391 and -0.524207391.Subproblem 1
x + -0.04545454546 = 0.524207391 Simplifying x + -0.04545454546 = 0.524207391 Reorder the terms: -0.04545454546 + x = 0.524207391 Solving -0.04545454546 + x = 0.524207391 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 = 0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = 0.524207391 + 0.04545454546 x = 0.524207391 + 0.04545454546 Combine like terms: 0.524207391 + 0.04545454546 = 0.56966193646 x = 0.56966193646 Simplifying x = 0.56966193646Subproblem 2
x + -0.04545454546 = -0.524207391 Simplifying x + -0.04545454546 = -0.524207391 Reorder the terms: -0.04545454546 + x = -0.524207391 Solving -0.04545454546 + x = -0.524207391 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 = -0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + x = -0.524207391 + 0.04545454546 x = -0.524207391 + 0.04545454546 Combine like terms: -0.524207391 + 0.04545454546 = -0.47875284554 x = -0.47875284554 Simplifying x = -0.47875284554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.56966193646, -0.47875284554}
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