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Simplifying (11x + 9)(11x + 9) = 110 Reorder the terms: (9 + 11x)(11x + 9) = 110 Reorder the terms: (9 + 11x)(9 + 11x) = 110 Multiply (9 + 11x) * (9 + 11x) (9(9 + 11x) + 11x * (9 + 11x)) = 110 ((9 * 9 + 11x * 9) + 11x * (9 + 11x)) = 110 ((81 + 99x) + 11x * (9 + 11x)) = 110 (81 + 99x + (9 * 11x + 11x * 11x)) = 110 (81 + 99x + (99x + 121x2)) = 110 Combine like terms: 99x + 99x = 198x (81 + 198x + 121x2) = 110 Solving 81 + 198x + 121x2 = 110 Solving for variable 'x'. Reorder the terms: 81 + -110 + 198x + 121x2 = 110 + -110 Combine like terms: 81 + -110 = -29 -29 + 198x + 121x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -29 + 198x + 121x2 = 0 Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -0.2396694215 + 1.636363636x + x2 = 0 Move the constant term to the right: Add '0.2396694215' to each side of the equation. -0.2396694215 + 1.636363636x + 0.2396694215 + x2 = 0 + 0.2396694215 Reorder the terms: -0.2396694215 + 0.2396694215 + 1.636363636x + x2 = 0 + 0.2396694215 Combine like terms: -0.2396694215 + 0.2396694215 = 0.0000000000 0.0000000000 + 1.636363636x + x2 = 0 + 0.2396694215 1.636363636x + x2 = 0 + 0.2396694215 Combine like terms: 0 + 0.2396694215 = 0.2396694215 1.636363636x + x2 = 0.2396694215 The x term is 1.636363636x. Take half its coefficient (0.818181818). Square it (0.6694214873) and add it to both sides. Add '0.6694214873' to each side of the equation. 1.636363636x + 0.6694214873 + x2 = 0.2396694215 + 0.6694214873 Reorder the terms: 0.6694214873 + 1.636363636x + x2 = 0.2396694215 + 0.6694214873 Combine like terms: 0.2396694215 + 0.6694214873 = 0.9090909088 0.6694214873 + 1.636363636x + x2 = 0.9090909088 Factor a perfect square on the left side: (x + 0.818181818)(x + 0.818181818) = 0.9090909088 Calculate the square root of the right side: 0.953462589 Break this problem into two subproblems by setting (x + 0.818181818) equal to 0.953462589 and -0.953462589.Subproblem 1
x + 0.818181818 = 0.953462589 Simplifying x + 0.818181818 = 0.953462589 Reorder the terms: 0.818181818 + x = 0.953462589 Solving 0.818181818 + x = 0.953462589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = 0.953462589 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = 0.953462589 + -0.818181818 x = 0.953462589 + -0.818181818 Combine like terms: 0.953462589 + -0.818181818 = 0.135280771 x = 0.135280771 Simplifying x = 0.135280771Subproblem 2
x + 0.818181818 = -0.953462589 Simplifying x + 0.818181818 = -0.953462589 Reorder the terms: 0.818181818 + x = -0.953462589 Solving 0.818181818 + x = -0.953462589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = -0.953462589 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = -0.953462589 + -0.818181818 x = -0.953462589 + -0.818181818 Combine like terms: -0.953462589 + -0.818181818 = -1.771644407 x = -1.771644407 Simplifying x = -1.771644407Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.135280771, -1.771644407}
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