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Simplifying 11x2 + -84x + 24 = 0 Reorder the terms: 24 + -84x + 11x2 = 0 Solving 24 + -84x + 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'. 2.181818182 + -7.636363636x + x2 = 0 Move the constant term to the right: Add '-2.181818182' to each side of the equation. 2.181818182 + -7.636363636x + -2.181818182 + x2 = 0 + -2.181818182 Reorder the terms: 2.181818182 + -2.181818182 + -7.636363636x + x2 = 0 + -2.181818182 Combine like terms: 2.181818182 + -2.181818182 = 0.000000000 0.000000000 + -7.636363636x + x2 = 0 + -2.181818182 -7.636363636x + x2 = 0 + -2.181818182 Combine like terms: 0 + -2.181818182 = -2.181818182 -7.636363636x + x2 = -2.181818182 The x term is -7.636363636x. Take half its coefficient (-3.818181818). Square it (14.57851240) and add it to both sides. Add '14.57851240' to each side of the equation. -7.636363636x + 14.57851240 + x2 = -2.181818182 + 14.57851240 Reorder the terms: 14.57851240 + -7.636363636x + x2 = -2.181818182 + 14.57851240 Combine like terms: -2.181818182 + 14.57851240 = 12.396694218 14.57851240 + -7.636363636x + x2 = 12.396694218 Factor a perfect square on the left side: (x + -3.818181818)(x + -3.818181818) = 12.396694218 Calculate the square root of the right side: 3.520893952 Break this problem into two subproblems by setting (x + -3.818181818) equal to 3.520893952 and -3.520893952.Subproblem 1
x + -3.818181818 = 3.520893952 Simplifying x + -3.818181818 = 3.520893952 Reorder the terms: -3.818181818 + x = 3.520893952 Solving -3.818181818 + x = 3.520893952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.818181818' to each side of the equation. -3.818181818 + 3.818181818 + x = 3.520893952 + 3.818181818 Combine like terms: -3.818181818 + 3.818181818 = 0.000000000 0.000000000 + x = 3.520893952 + 3.818181818 x = 3.520893952 + 3.818181818 Combine like terms: 3.520893952 + 3.818181818 = 7.33907577 x = 7.33907577 Simplifying x = 7.33907577Subproblem 2
x + -3.818181818 = -3.520893952 Simplifying x + -3.818181818 = -3.520893952 Reorder the terms: -3.818181818 + x = -3.520893952 Solving -3.818181818 + x = -3.520893952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.818181818' to each side of the equation. -3.818181818 + 3.818181818 + x = -3.520893952 + 3.818181818 Combine like terms: -3.818181818 + 3.818181818 = 0.000000000 0.000000000 + x = -3.520893952 + 3.818181818 x = -3.520893952 + 3.818181818 Combine like terms: -3.520893952 + 3.818181818 = 0.297287866 x = 0.297287866 Simplifying x = 0.297287866Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.33907577, 0.297287866}
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