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Simplifying 6x2 + -11x + -60 = 0 Reorder the terms: -60 + -11x + 6x2 = 0 Solving -60 + -11x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.833333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1.833333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.833333333x + x2 = 0 + 10 -1.833333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.833333333x + x2 = 10 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 10 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 10 + 0.8402777775 Combine like terms: 10 + 0.8402777775 = 10.8402777775 0.8402777775 + -1.833333333x + x2 = 10.8402777775 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 10.8402777775 Calculate the square root of the right side: 3.292457711 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 3.292457711 and -3.292457711.Subproblem 1
x + -0.9166666665 = 3.292457711 Simplifying x + -0.9166666665 = 3.292457711 Reorder the terms: -0.9166666665 + x = 3.292457711 Solving -0.9166666665 + x = 3.292457711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 3.292457711 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 3.292457711 + 0.9166666665 x = 3.292457711 + 0.9166666665 Combine like terms: 3.292457711 + 0.9166666665 = 4.2091243775 x = 4.2091243775 Simplifying x = 4.2091243775Subproblem 2
x + -0.9166666665 = -3.292457711 Simplifying x + -0.9166666665 = -3.292457711 Reorder the terms: -0.9166666665 + x = -3.292457711 Solving -0.9166666665 + x = -3.292457711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -3.292457711 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -3.292457711 + 0.9166666665 x = -3.292457711 + 0.9166666665 Combine like terms: -3.292457711 + 0.9166666665 = -2.3757910445 x = -2.3757910445 Simplifying x = -2.3757910445Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2091243775, -2.3757910445}
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