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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 = 0.1702712132 x = 0.1702712132 Simplifying x = 0.1702712132Subproblem 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 = -0.5339075768 x = -0.5339075768 Simplifying x = -0.5339075768Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1702712132, -0.5339075768}
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