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Simplifying 11x2 + -20x + -52 = 0 Reorder the terms: -52 + -20x + 11x2 = 0 Solving -52 + -20x + 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'. -4.727272727 + -1.818181818x + x2 = 0 Move the constant term to the right: Add '4.727272727' to each side of the equation. -4.727272727 + -1.818181818x + 4.727272727 + x2 = 0 + 4.727272727 Reorder the terms: -4.727272727 + 4.727272727 + -1.818181818x + x2 = 0 + 4.727272727 Combine like terms: -4.727272727 + 4.727272727 = 0.000000000 0.000000000 + -1.818181818x + x2 = 0 + 4.727272727 -1.818181818x + x2 = 0 + 4.727272727 Combine like terms: 0 + 4.727272727 = 4.727272727 -1.818181818x + x2 = 4.727272727 The x term is -1.818181818x. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818x + 0.8264462808 + x2 = 4.727272727 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818x + x2 = 4.727272727 + 0.8264462808 Combine like terms: 4.727272727 + 0.8264462808 = 5.5537190078 0.8264462808 + -1.818181818x + x2 = 5.5537190078 Factor a perfect square on the left side: (x + -0.909090909)(x + -0.909090909) = 5.5537190078 Calculate the square root of the right side: 2.356632981 Break this problem into two subproblems by setting (x + -0.909090909) equal to 2.356632981 and -2.356632981.Subproblem 1
x + -0.909090909 = 2.356632981 Simplifying x + -0.909090909 = 2.356632981 Reorder the terms: -0.909090909 + x = 2.356632981 Solving -0.909090909 + x = 2.356632981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = 2.356632981 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = 2.356632981 + 0.909090909 x = 2.356632981 + 0.909090909 Combine like terms: 2.356632981 + 0.909090909 = 3.26572389 x = 3.26572389 Simplifying x = 3.26572389Subproblem 2
x + -0.909090909 = -2.356632981 Simplifying x + -0.909090909 = -2.356632981 Reorder the terms: -0.909090909 + x = -2.356632981 Solving -0.909090909 + x = -2.356632981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = -2.356632981 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = -2.356632981 + 0.909090909 x = -2.356632981 + 0.909090909 Combine like terms: -2.356632981 + 0.909090909 = -1.447542072 x = -1.447542072 Simplifying x = -1.447542072Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.26572389, -1.447542072}
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