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Simplifying 11x2 + -17x + -20 = 0 Reorder the terms: -20 + -17x + 11x2 = 0 Solving -20 + -17x + 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'. -1.818181818 + -1.545454545x + x2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + -1.545454545x + 1.818181818 + x2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + -1.545454545x + x2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + -1.545454545x + x2 = 0 + 1.818181818 -1.545454545x + x2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 -1.545454545x + x2 = 1.818181818 The x term is -1.545454545x. Take half its coefficient (-0.7727272725). Square it (0.5971074377) and add it to both sides. Add '0.5971074377' to each side of the equation. -1.545454545x + 0.5971074377 + x2 = 1.818181818 + 0.5971074377 Reorder the terms: 0.5971074377 + -1.545454545x + x2 = 1.818181818 + 0.5971074377 Combine like terms: 1.818181818 + 0.5971074377 = 2.4152892557 0.5971074377 + -1.545454545x + x2 = 2.4152892557 Factor a perfect square on the left side: (x + -0.7727272725)(x + -0.7727272725) = 2.4152892557 Calculate the square root of the right side: 1.554120091 Break this problem into two subproblems by setting (x + -0.7727272725) equal to 1.554120091 and -1.554120091.Subproblem 1
x + -0.7727272725 = 1.554120091 Simplifying x + -0.7727272725 = 1.554120091 Reorder the terms: -0.7727272725 + x = 1.554120091 Solving -0.7727272725 + x = 1.554120091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7727272725' to each side of the equation. -0.7727272725 + 0.7727272725 + x = 1.554120091 + 0.7727272725 Combine like terms: -0.7727272725 + 0.7727272725 = 0.0000000000 0.0000000000 + x = 1.554120091 + 0.7727272725 x = 1.554120091 + 0.7727272725 Combine like terms: 1.554120091 + 0.7727272725 = 2.3268473635 x = 2.3268473635 Simplifying x = 2.3268473635Subproblem 2
x + -0.7727272725 = -1.554120091 Simplifying x + -0.7727272725 = -1.554120091 Reorder the terms: -0.7727272725 + x = -1.554120091 Solving -0.7727272725 + x = -1.554120091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7727272725' to each side of the equation. -0.7727272725 + 0.7727272725 + x = -1.554120091 + 0.7727272725 Combine like terms: -0.7727272725 + 0.7727272725 = 0.0000000000 0.0000000000 + x = -1.554120091 + 0.7727272725 x = -1.554120091 + 0.7727272725 Combine like terms: -1.554120091 + 0.7727272725 = -0.7813928185 x = -0.7813928185 Simplifying x = -0.7813928185Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3268473635, -0.7813928185}
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