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Simplifying 11x2 + -60x + 50 = 0 Reorder the terms: 50 + -60x + 11x2 = 0 Solving 50 + -60x + 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'. 4.545454545 + -5.454545455x + x2 = 0 Move the constant term to the right: Add '-4.545454545' to each side of the equation. 4.545454545 + -5.454545455x + -4.545454545 + x2 = 0 + -4.545454545 Reorder the terms: 4.545454545 + -4.545454545 + -5.454545455x + x2 = 0 + -4.545454545 Combine like terms: 4.545454545 + -4.545454545 = 0.000000000 0.000000000 + -5.454545455x + x2 = 0 + -4.545454545 -5.454545455x + x2 = 0 + -4.545454545 Combine like terms: 0 + -4.545454545 = -4.545454545 -5.454545455x + x2 = -4.545454545 The x term is -5.454545455x. Take half its coefficient (-2.727272728). Square it (7.438016533) and add it to both sides. Add '7.438016533' to each side of the equation. -5.454545455x + 7.438016533 + x2 = -4.545454545 + 7.438016533 Reorder the terms: 7.438016533 + -5.454545455x + x2 = -4.545454545 + 7.438016533 Combine like terms: -4.545454545 + 7.438016533 = 2.892561988 7.438016533 + -5.454545455x + x2 = 2.892561988 Factor a perfect square on the left side: (x + -2.727272728)(x + -2.727272728) = 2.892561988 Calculate the square root of the right side: 1.700753359 Break this problem into two subproblems by setting (x + -2.727272728) equal to 1.700753359 and -1.700753359.Subproblem 1
x + -2.727272728 = 1.700753359 Simplifying x + -2.727272728 = 1.700753359 Reorder the terms: -2.727272728 + x = 1.700753359 Solving -2.727272728 + x = 1.700753359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.727272728' to each side of the equation. -2.727272728 + 2.727272728 + x = 1.700753359 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = 1.700753359 + 2.727272728 x = 1.700753359 + 2.727272728 Combine like terms: 1.700753359 + 2.727272728 = 4.428026087 x = 4.428026087 Simplifying x = 4.428026087Subproblem 2
x + -2.727272728 = -1.700753359 Simplifying x + -2.727272728 = -1.700753359 Reorder the terms: -2.727272728 + x = -1.700753359 Solving -2.727272728 + x = -1.700753359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.727272728' to each side of the equation. -2.727272728 + 2.727272728 + x = -1.700753359 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = -1.700753359 + 2.727272728 x = -1.700753359 + 2.727272728 Combine like terms: -1.700753359 + 2.727272728 = 1.026519369 x = 1.026519369 Simplifying x = 1.026519369Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.428026087, 1.026519369}
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