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Simplifying 11x2 + -60x + -64 = 0 Reorder the terms: -64 + -60x + 11x2 = 0 Solving -64 + -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'. -5.818181818 + -5.454545455x + x2 = 0 Move the constant term to the right: Add '5.818181818' to each side of the equation. -5.818181818 + -5.454545455x + 5.818181818 + x2 = 0 + 5.818181818 Reorder the terms: -5.818181818 + 5.818181818 + -5.454545455x + x2 = 0 + 5.818181818 Combine like terms: -5.818181818 + 5.818181818 = 0.000000000 0.000000000 + -5.454545455x + x2 = 0 + 5.818181818 -5.454545455x + x2 = 0 + 5.818181818 Combine like terms: 0 + 5.818181818 = 5.818181818 -5.454545455x + x2 = 5.818181818 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 = 5.818181818 + 7.438016533 Reorder the terms: 7.438016533 + -5.454545455x + x2 = 5.818181818 + 7.438016533 Combine like terms: 5.818181818 + 7.438016533 = 13.256198351 7.438016533 + -5.454545455x + x2 = 13.256198351 Factor a perfect square on the left side: (x + -2.727272728)(x + -2.727272728) = 13.256198351 Calculate the square root of the right side: 3.640906254 Break this problem into two subproblems by setting (x + -2.727272728) equal to 3.640906254 and -3.640906254.Subproblem 1
x + -2.727272728 = 3.640906254 Simplifying x + -2.727272728 = 3.640906254 Reorder the terms: -2.727272728 + x = 3.640906254 Solving -2.727272728 + x = 3.640906254 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 = 3.640906254 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = 3.640906254 + 2.727272728 x = 3.640906254 + 2.727272728 Combine like terms: 3.640906254 + 2.727272728 = 6.368178982 x = 6.368178982 Simplifying x = 6.368178982Subproblem 2
x + -2.727272728 = -3.640906254 Simplifying x + -2.727272728 = -3.640906254 Reorder the terms: -2.727272728 + x = -3.640906254 Solving -2.727272728 + x = -3.640906254 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 = -3.640906254 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = -3.640906254 + 2.727272728 x = -3.640906254 + 2.727272728 Combine like terms: -3.640906254 + 2.727272728 = -0.913633526 x = -0.913633526 Simplifying x = -0.913633526Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.368178982, -0.913633526}
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