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Simplifying 6x2 + -11x + -10 = 8 Reorder the terms: -10 + -11x + 6x2 = 8 Solving -10 + -11x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: -10 + -8 + -11x + 6x2 = 8 + -8 Combine like terms: -10 + -8 = -18 -18 + -11x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -18 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.833333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.833333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.833333333x + x2 = 0 + 3 -1.833333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.833333333x + x2 = 3 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 = 3 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 3 + 0.8402777775 Combine like terms: 3 + 0.8402777775 = 3.8402777775 0.8402777775 + -1.833333333x + x2 = 3.8402777775 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 3.8402777775 Calculate the square root of the right side: 1.959662669 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.959662669 and -1.959662669.Subproblem 1
x + -0.9166666665 = 1.959662669 Simplifying x + -0.9166666665 = 1.959662669 Reorder the terms: -0.9166666665 + x = 1.959662669 Solving -0.9166666665 + x = 1.959662669 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 = 1.959662669 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.959662669 + 0.9166666665 x = 1.959662669 + 0.9166666665 Combine like terms: 1.959662669 + 0.9166666665 = 2.8763293355 x = 2.8763293355 Simplifying x = 2.8763293355Subproblem 2
x + -0.9166666665 = -1.959662669 Simplifying x + -0.9166666665 = -1.959662669 Reorder the terms: -0.9166666665 + x = -1.959662669 Solving -0.9166666665 + x = -1.959662669 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 = -1.959662669 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.959662669 + 0.9166666665 x = -1.959662669 + 0.9166666665 Combine like terms: -1.959662669 + 0.9166666665 = -1.0429960025 x = -1.0429960025 Simplifying x = -1.0429960025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8763293355, -1.0429960025}
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