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Simplifying 11x2 + -6x + -16 = 0 Reorder the terms: -16 + -6x + 11x2 = 0 Solving -16 + -6x + 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'. -1.454545455 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '1.454545455' to each side of the equation. -1.454545455 + -0.5454545455x + 1.454545455 + x2 = 0 + 1.454545455 Reorder the terms: -1.454545455 + 1.454545455 + -0.5454545455x + x2 = 0 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + -0.5454545455x + x2 = 0 + 1.454545455 -0.5454545455x + x2 = 0 + 1.454545455 Combine like terms: 0 + 1.454545455 = 1.454545455 -0.5454545455x + x2 = 1.454545455 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 1.454545455 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 1.454545455 + 0.07438016533 Combine like terms: 1.454545455 + 0.07438016533 = 1.52892562033 0.07438016533 + -0.5454545455x + x2 = 1.52892562033 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 1.52892562033 Calculate the square root of the right side: 1.236497319 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 1.236497319 and -1.236497319.Subproblem 1
x + -0.2727272728 = 1.236497319 Simplifying x + -0.2727272728 = 1.236497319 Reorder the terms: -0.2727272728 + x = 1.236497319 Solving -0.2727272728 + x = 1.236497319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 1.236497319 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 1.236497319 + 0.2727272728 x = 1.236497319 + 0.2727272728 Combine like terms: 1.236497319 + 0.2727272728 = 1.5092245918 x = 1.5092245918 Simplifying x = 1.5092245918Subproblem 2
x + -0.2727272728 = -1.236497319 Simplifying x + -0.2727272728 = -1.236497319 Reorder the terms: -0.2727272728 + x = -1.236497319 Solving -0.2727272728 + x = -1.236497319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -1.236497319 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -1.236497319 + 0.2727272728 x = -1.236497319 + 0.2727272728 Combine like terms: -1.236497319 + 0.2727272728 = -0.9637700462 x = -0.9637700462 Simplifying x = -0.9637700462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5092245918, -0.9637700462}
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