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Simplifying 6x2 + 11x + -27 = 0 Reorder the terms: -27 + 11x + 6x2 = 0 Solving -27 + 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'. -4.5 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.833333333x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.833333333x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.833333333x + x2 = 0 + 4.5 1.833333333x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.833333333x + x2 = 4.5 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 = 4.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 4.5 + 0.8402777775 Combine like terms: 4.5 + 0.8402777775 = 5.3402777775 0.8402777775 + 1.833333333x + x2 = 5.3402777775 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 5.3402777775 Calculate the square root of the right side: 2.310904104 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 2.310904104 and -2.310904104.Subproblem 1
x + 0.9166666665 = 2.310904104 Simplifying x + 0.9166666665 = 2.310904104 Reorder the terms: 0.9166666665 + x = 2.310904104 Solving 0.9166666665 + x = 2.310904104 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 = 2.310904104 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 2.310904104 + -0.9166666665 x = 2.310904104 + -0.9166666665 Combine like terms: 2.310904104 + -0.9166666665 = 1.3942374375 x = 1.3942374375 Simplifying x = 1.3942374375Subproblem 2
x + 0.9166666665 = -2.310904104 Simplifying x + 0.9166666665 = -2.310904104 Reorder the terms: 0.9166666665 + x = -2.310904104 Solving 0.9166666665 + x = -2.310904104 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 = -2.310904104 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -2.310904104 + -0.9166666665 x = -2.310904104 + -0.9166666665 Combine like terms: -2.310904104 + -0.9166666665 = -3.2275707705 x = -3.2275707705 Simplifying x = -3.2275707705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3942374375, -3.2275707705}
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