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Simplifying 11x2 + -4x + -8 = 0 Reorder the terms: -8 + -4x + 11x2 = 0 Solving -8 + -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'. -0.7272727273 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.3636363636x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.3636363636x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.3636363636x + x2 = 0 + 0.7272727273 -0.3636363636x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.3636363636x + x2 = 0.7272727273 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 = 0.7272727273 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.7272727273 + 0.03305785123 Combine like terms: 0.7272727273 + 0.03305785123 = 0.76033057853 0.03305785123 + -0.3636363636x + x2 = 0.76033057853 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.76033057853 Calculate the square root of the right side: 0.871969368 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.871969368 and -0.871969368.Subproblem 1
x + -0.1818181818 = 0.871969368 Simplifying x + -0.1818181818 = 0.871969368 Reorder the terms: -0.1818181818 + x = 0.871969368 Solving -0.1818181818 + x = 0.871969368 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 = 0.871969368 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.871969368 + 0.1818181818 x = 0.871969368 + 0.1818181818 Combine like terms: 0.871969368 + 0.1818181818 = 1.0537875498 x = 1.0537875498 Simplifying x = 1.0537875498Subproblem 2
x + -0.1818181818 = -0.871969368 Simplifying x + -0.1818181818 = -0.871969368 Reorder the terms: -0.1818181818 + x = -0.871969368 Solving -0.1818181818 + x = -0.871969368 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 = -0.871969368 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.871969368 + 0.1818181818 x = -0.871969368 + 0.1818181818 Combine like terms: -0.871969368 + 0.1818181818 = -0.6901511862 x = -0.6901511862 Simplifying x = -0.6901511862Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0537875498, -0.6901511862}
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