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Simplifying 11x2 + 20x + -2 = 0 Reorder the terms: -2 + 20x + 11x2 = 0 Solving -2 + 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'. -0.1818181818 + 1.818181818x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 1.818181818x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 1.818181818x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 1.818181818x + x2 = 0 + 0.1818181818 1.818181818x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 1.818181818x + x2 = 0.1818181818 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 = 0.1818181818 + 0.8264462808 Reorder the terms: 0.8264462808 + 1.818181818x + x2 = 0.1818181818 + 0.8264462808 Combine like terms: 0.1818181818 + 0.8264462808 = 1.0082644626 0.8264462808 + 1.818181818x + x2 = 1.0082644626 Factor a perfect square on the left side: (x + 0.909090909)(x + 0.909090909) = 1.0082644626 Calculate the square root of the right side: 1.004123729 Break this problem into two subproblems by setting (x + 0.909090909) equal to 1.004123729 and -1.004123729.Subproblem 1
x + 0.909090909 = 1.004123729 Simplifying x + 0.909090909 = 1.004123729 Reorder the terms: 0.909090909 + x = 1.004123729 Solving 0.909090909 + x = 1.004123729 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 = 1.004123729 + -0.909090909 Combine like terms: 0.909090909 + -0.909090909 = 0.000000000 0.000000000 + x = 1.004123729 + -0.909090909 x = 1.004123729 + -0.909090909 Combine like terms: 1.004123729 + -0.909090909 = 0.09503282 x = 0.09503282 Simplifying x = 0.09503282Subproblem 2
x + 0.909090909 = -1.004123729 Simplifying x + 0.909090909 = -1.004123729 Reorder the terms: 0.909090909 + x = -1.004123729 Solving 0.909090909 + x = -1.004123729 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 = -1.004123729 + -0.909090909 Combine like terms: 0.909090909 + -0.909090909 = 0.000000000 0.000000000 + x = -1.004123729 + -0.909090909 x = -1.004123729 + -0.909090909 Combine like terms: -1.004123729 + -0.909090909 = -1.913214638 x = -1.913214638 Simplifying x = -1.913214638Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.09503282, -1.913214638}
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