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Simplifying 11x2 + -4x = 1 Reorder the terms: -4x + 11x2 = 1 Solving -4x + 11x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -4x + 11x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.3636363636x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.3636363636x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.3636363636x + x2 = 0 + 0.09090909091 -0.3636363636x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.3636363636x + x2 = 0.09090909091 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 = 0.09090909091 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.09090909091 + 0.03305785123 Combine like terms: 0.09090909091 + 0.03305785123 = 0.12396694214 0.03305785123 + -0.3636363636x + x2 = 0.12396694214 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.12396694214 Calculate the square root of the right side: 0.352089395 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.352089395 and -0.352089395.Subproblem 1
x + -0.1818181818 = 0.352089395 Simplifying x + -0.1818181818 = 0.352089395 Reorder the terms: -0.1818181818 + x = 0.352089395 Solving -0.1818181818 + x = 0.352089395 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 = 0.352089395 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.352089395 + 0.1818181818 x = 0.352089395 + 0.1818181818 Combine like terms: 0.352089395 + 0.1818181818 = 0.5339075768 x = 0.5339075768 Simplifying x = 0.5339075768Subproblem 2
x + -0.1818181818 = -0.352089395 Simplifying x + -0.1818181818 = -0.352089395 Reorder the terms: -0.1818181818 + x = -0.352089395 Solving -0.1818181818 + x = -0.352089395 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 = -0.352089395 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.352089395 + 0.1818181818 x = -0.352089395 + 0.1818181818 Combine like terms: -0.352089395 + 0.1818181818 = -0.1702712132 x = -0.1702712132 Simplifying x = -0.1702712132Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5339075768, -0.1702712132}
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