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Simplifying x = -11x(x) + -3x + 10 Multiply x * x x = -11x2 + -3x + 10 Reorder the terms: x = 10 + -3x + -11x2 Solving x = 10 + -3x + -11x2 Solving for variable 'x'. Reorder the terms: -10 + x + 3x + 11x2 = 10 + -3x + -11x2 + -10 + 3x + 11x2 Combine like terms: x + 3x = 4x -10 + 4x + 11x2 = 10 + -3x + -11x2 + -10 + 3x + 11x2 Reorder the terms: -10 + 4x + 11x2 = 10 + -10 + -3x + 3x + -11x2 + 11x2 Combine like terms: 10 + -10 = 0 -10 + 4x + 11x2 = 0 + -3x + 3x + -11x2 + 11x2 -10 + 4x + 11x2 = -3x + 3x + -11x2 + 11x2 Combine like terms: -3x + 3x = 0 -10 + 4x + 11x2 = 0 + -11x2 + 11x2 -10 + 4x + 11x2 = -11x2 + 11x2 Combine like terms: -11x2 + 11x2 = 0 -10 + 4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + 0.3636363636x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + 0.3636363636x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + 0.3636363636x + x2 = 0 + 0.9090909091 0.3636363636x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 0.3636363636x + x2 = 0.9090909091 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 = 0.9090909091 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 0.9090909091 + 0.03305785123 Combine like terms: 0.9090909091 + 0.03305785123 = 0.94214876033 0.03305785123 + 0.3636363636x + x2 = 0.94214876033 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 0.94214876033 Calculate the square root of the right side: 0.970643477 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 0.970643477 and -0.970643477.Subproblem 1
x + 0.1818181818 = 0.970643477 Simplifying x + 0.1818181818 = 0.970643477 Reorder the terms: 0.1818181818 + x = 0.970643477 Solving 0.1818181818 + x = 0.970643477 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 = 0.970643477 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 0.970643477 + -0.1818181818 x = 0.970643477 + -0.1818181818 Combine like terms: 0.970643477 + -0.1818181818 = 0.7888252952 x = 0.7888252952 Simplifying x = 0.7888252952Subproblem 2
x + 0.1818181818 = -0.970643477 Simplifying x + 0.1818181818 = -0.970643477 Reorder the terms: 0.1818181818 + x = -0.970643477 Solving 0.1818181818 + x = -0.970643477 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 = -0.970643477 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -0.970643477 + -0.1818181818 x = -0.970643477 + -0.1818181818 Combine like terms: -0.970643477 + -0.1818181818 = -1.1524616588 x = -1.1524616588 Simplifying x = -1.1524616588Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7888252952, -1.1524616588}
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