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Simplifying 6x2 + -11x + -256 = 0 Reorder the terms: -256 + -11x + 6x2 = 0 Solving -256 + -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'. -42.66666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '42.66666667' to each side of the equation. -42.66666667 + -1.833333333x + 42.66666667 + x2 = 0 + 42.66666667 Reorder the terms: -42.66666667 + 42.66666667 + -1.833333333x + x2 = 0 + 42.66666667 Combine like terms: -42.66666667 + 42.66666667 = 0.00000000 0.00000000 + -1.833333333x + x2 = 0 + 42.66666667 -1.833333333x + x2 = 0 + 42.66666667 Combine like terms: 0 + 42.66666667 = 42.66666667 -1.833333333x + x2 = 42.66666667 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 = 42.66666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 42.66666667 + 0.8402777775 Combine like terms: 42.66666667 + 0.8402777775 = 43.5069444475 0.8402777775 + -1.833333333x + x2 = 43.5069444475 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 43.5069444475 Calculate the square root of the right side: 6.595979415 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 6.595979415 and -6.595979415.Subproblem 1
x + -0.9166666665 = 6.595979415 Simplifying x + -0.9166666665 = 6.595979415 Reorder the terms: -0.9166666665 + x = 6.595979415 Solving -0.9166666665 + x = 6.595979415 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 = 6.595979415 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 6.595979415 + 0.9166666665 x = 6.595979415 + 0.9166666665 Combine like terms: 6.595979415 + 0.9166666665 = 7.5126460815 x = 7.5126460815 Simplifying x = 7.5126460815Subproblem 2
x + -0.9166666665 = -6.595979415 Simplifying x + -0.9166666665 = -6.595979415 Reorder the terms: -0.9166666665 + x = -6.595979415 Solving -0.9166666665 + x = -6.595979415 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 = -6.595979415 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -6.595979415 + 0.9166666665 x = -6.595979415 + 0.9166666665 Combine like terms: -6.595979415 + 0.9166666665 = -5.6793127485 x = -5.6793127485 Simplifying x = -5.6793127485Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.5126460815, -5.6793127485}
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