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Simplifying 11x2 + 49x + -24 = 0 Reorder the terms: -24 + 49x + 11x2 = 0 Solving -24 + 49x + 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 + 4.454545455x + x2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + 4.454545455x + 2.181818182 + x2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + 4.454545455x + x2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + 4.454545455x + x2 = 0 + 2.181818182 4.454545455x + x2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 4.454545455x + x2 = 2.181818182 The x term is 4.454545455x. Take half its coefficient (2.227272728). Square it (4.960743805) and add it to both sides. Add '4.960743805' to each side of the equation. 4.454545455x + 4.960743805 + x2 = 2.181818182 + 4.960743805 Reorder the terms: 4.960743805 + 4.454545455x + x2 = 2.181818182 + 4.960743805 Combine like terms: 2.181818182 + 4.960743805 = 7.142561987 4.960743805 + 4.454545455x + x2 = 7.142561987 Factor a perfect square on the left side: (x + 2.227272728)(x + 2.227272728) = 7.142561987 Calculate the square root of the right side: 2.6725572 Break this problem into two subproblems by setting (x + 2.227272728) equal to 2.6725572 and -2.6725572.Subproblem 1
x + 2.227272728 = 2.6725572 Simplifying x + 2.227272728 = 2.6725572 Reorder the terms: 2.227272728 + x = 2.6725572 Solving 2.227272728 + x = 2.6725572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.227272728' to each side of the equation. 2.227272728 + -2.227272728 + x = 2.6725572 + -2.227272728 Combine like terms: 2.227272728 + -2.227272728 = 0.000000000 0.000000000 + x = 2.6725572 + -2.227272728 x = 2.6725572 + -2.227272728 Combine like terms: 2.6725572 + -2.227272728 = 0.445284472 x = 0.445284472 Simplifying x = 0.445284472Subproblem 2
x + 2.227272728 = -2.6725572 Simplifying x + 2.227272728 = -2.6725572 Reorder the terms: 2.227272728 + x = -2.6725572 Solving 2.227272728 + x = -2.6725572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.227272728' to each side of the equation. 2.227272728 + -2.227272728 + x = -2.6725572 + -2.227272728 Combine like terms: 2.227272728 + -2.227272728 = 0.000000000 0.000000000 + x = -2.6725572 + -2.227272728 x = -2.6725572 + -2.227272728 Combine like terms: -2.6725572 + -2.227272728 = -4.899829928 x = -4.899829928 Simplifying x = -4.899829928Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.445284472, -4.899829928}
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