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Simplifying 11x2 + -4x + -3 = 0 Reorder the terms: -3 + -4x + 11x2 = 0 Solving -3 + -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'. -0.2727272727 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.3636363636x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.3636363636x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.3636363636x + x2 = 0 + 0.2727272727 -0.3636363636x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.3636363636x + x2 = 0.2727272727 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 = 0.2727272727 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.2727272727 + 0.03305785123 Combine like terms: 0.2727272727 + 0.03305785123 = 0.30578512393 0.03305785123 + -0.3636363636x + x2 = 0.30578512393 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.30578512393 Calculate the square root of the right side: 0.552978412 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.552978412 and -0.552978412.Subproblem 1
x + -0.1818181818 = 0.552978412 Simplifying x + -0.1818181818 = 0.552978412 Reorder the terms: -0.1818181818 + x = 0.552978412 Solving -0.1818181818 + x = 0.552978412 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 = 0.552978412 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.552978412 + 0.1818181818 x = 0.552978412 + 0.1818181818 Combine like terms: 0.552978412 + 0.1818181818 = 0.7347965938 x = 0.7347965938 Simplifying x = 0.7347965938Subproblem 2
x + -0.1818181818 = -0.552978412 Simplifying x + -0.1818181818 = -0.552978412 Reorder the terms: -0.1818181818 + x = -0.552978412 Solving -0.1818181818 + x = -0.552978412 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 = -0.552978412 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.552978412 + 0.1818181818 x = -0.552978412 + 0.1818181818 Combine like terms: -0.552978412 + 0.1818181818 = -0.3711602302 x = -0.3711602302 Simplifying x = -0.3711602302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7347965938, -0.3711602302}
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