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Simplifying 11x2 + -22.6x + 1.69 = 0 Reorder the terms: 1.69 + -22.6x + 11x2 = 0 Solving 1.69 + -22.6x + 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'. 0.1536363636 + -2.054545455x + x2 = 0 Move the constant term to the right: Add '-0.1536363636' to each side of the equation. 0.1536363636 + -2.054545455x + -0.1536363636 + x2 = 0 + -0.1536363636 Reorder the terms: 0.1536363636 + -0.1536363636 + -2.054545455x + x2 = 0 + -0.1536363636 Combine like terms: 0.1536363636 + -0.1536363636 = 0.0000000000 0.0000000000 + -2.054545455x + x2 = 0 + -0.1536363636 -2.054545455x + x2 = 0 + -0.1536363636 Combine like terms: 0 + -0.1536363636 = -0.1536363636 -2.054545455x + x2 = -0.1536363636 The x term is -2.054545455x. Take half its coefficient (-1.027272728). Square it (1.055289258) and add it to both sides. Add '1.055289258' to each side of the equation. -2.054545455x + 1.055289258 + x2 = -0.1536363636 + 1.055289258 Reorder the terms: 1.055289258 + -2.054545455x + x2 = -0.1536363636 + 1.055289258 Combine like terms: -0.1536363636 + 1.055289258 = 0.9016528944 1.055289258 + -2.054545455x + x2 = 0.9016528944 Factor a perfect square on the left side: (x + -1.027272728)(x + -1.027272728) = 0.9016528944 Calculate the square root of the right side: 0.94955405 Break this problem into two subproblems by setting (x + -1.027272728) equal to 0.94955405 and -0.94955405.Subproblem 1
x + -1.027272728 = 0.94955405 Simplifying x + -1.027272728 = 0.94955405 Reorder the terms: -1.027272728 + x = 0.94955405 Solving -1.027272728 + x = 0.94955405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027272728' to each side of the equation. -1.027272728 + 1.027272728 + x = 0.94955405 + 1.027272728 Combine like terms: -1.027272728 + 1.027272728 = 0.000000000 0.000000000 + x = 0.94955405 + 1.027272728 x = 0.94955405 + 1.027272728 Combine like terms: 0.94955405 + 1.027272728 = 1.976826778 x = 1.976826778 Simplifying x = 1.976826778Subproblem 2
x + -1.027272728 = -0.94955405 Simplifying x + -1.027272728 = -0.94955405 Reorder the terms: -1.027272728 + x = -0.94955405 Solving -1.027272728 + x = -0.94955405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027272728' to each side of the equation. -1.027272728 + 1.027272728 + x = -0.94955405 + 1.027272728 Combine like terms: -1.027272728 + 1.027272728 = 0.000000000 0.000000000 + x = -0.94955405 + 1.027272728 x = -0.94955405 + 1.027272728 Combine like terms: -0.94955405 + 1.027272728 = 0.077718678 x = 0.077718678 Simplifying x = 0.077718678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.976826778, 0.077718678}
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