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Simplifying 11x2 + -60x + -30 = 0 Reorder the terms: -30 + -60x + 11x2 = 0 Solving -30 + -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'. -2.727272727 + -5.454545455x + x2 = 0 Move the constant term to the right: Add '2.727272727' to each side of the equation. -2.727272727 + -5.454545455x + 2.727272727 + x2 = 0 + 2.727272727 Reorder the terms: -2.727272727 + 2.727272727 + -5.454545455x + x2 = 0 + 2.727272727 Combine like terms: -2.727272727 + 2.727272727 = 0.000000000 0.000000000 + -5.454545455x + x2 = 0 + 2.727272727 -5.454545455x + x2 = 0 + 2.727272727 Combine like terms: 0 + 2.727272727 = 2.727272727 -5.454545455x + x2 = 2.727272727 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 = 2.727272727 + 7.438016533 Reorder the terms: 7.438016533 + -5.454545455x + x2 = 2.727272727 + 7.438016533 Combine like terms: 2.727272727 + 7.438016533 = 10.16528926 7.438016533 + -5.454545455x + x2 = 10.16528926 Factor a perfect square on the left side: (x + -2.727272728)(x + -2.727272728) = 10.16528926 Calculate the square root of the right side: 3.188305076 Break this problem into two subproblems by setting (x + -2.727272728) equal to 3.188305076 and -3.188305076.Subproblem 1
x + -2.727272728 = 3.188305076 Simplifying x + -2.727272728 = 3.188305076 Reorder the terms: -2.727272728 + x = 3.188305076 Solving -2.727272728 + x = 3.188305076 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 = 3.188305076 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = 3.188305076 + 2.727272728 x = 3.188305076 + 2.727272728 Combine like terms: 3.188305076 + 2.727272728 = 5.915577804 x = 5.915577804 Simplifying x = 5.915577804Subproblem 2
x + -2.727272728 = -3.188305076 Simplifying x + -2.727272728 = -3.188305076 Reorder the terms: -2.727272728 + x = -3.188305076 Solving -2.727272728 + x = -3.188305076 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 = -3.188305076 + 2.727272728 Combine like terms: -2.727272728 + 2.727272728 = 0.000000000 0.000000000 + x = -3.188305076 + 2.727272728 x = -3.188305076 + 2.727272728 Combine like terms: -3.188305076 + 2.727272728 = -0.461032348 x = -0.461032348 Simplifying x = -0.461032348Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.915577804, -0.461032348}
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