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Simplifying (3x + -1)(2x + 6) = 5x Reorder the terms: (-1 + 3x)(2x + 6) = 5x Reorder the terms: (-1 + 3x)(6 + 2x) = 5x Multiply (-1 + 3x) * (6 + 2x) (-1(6 + 2x) + 3x * (6 + 2x)) = 5x ((6 * -1 + 2x * -1) + 3x * (6 + 2x)) = 5x ((-6 + -2x) + 3x * (6 + 2x)) = 5x (-6 + -2x + (6 * 3x + 2x * 3x)) = 5x (-6 + -2x + (18x + 6x2)) = 5x Combine like terms: -2x + 18x = 16x (-6 + 16x + 6x2) = 5x Solving -6 + 16x + 6x2 = 5x Solving for variable 'x'. Reorder the terms: -6 + 16x + -5x + 6x2 = 5x + -5x Combine like terms: 16x + -5x = 11x -6 + 11x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -6 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.833333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.833333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.833333333x + x2 = 0 + 1 1.833333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.833333333x + x2 = 1 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 = 1 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 1 + 0.8402777775 Combine like terms: 1 + 0.8402777775 = 1.8402777775 0.8402777775 + 1.833333333x + x2 = 1.8402777775 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 1.8402777775 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.356568383 and -1.356568383.Subproblem 1
x + 0.9166666665 = 1.356568383 Simplifying x + 0.9166666665 = 1.356568383 Reorder the terms: 0.9166666665 + x = 1.356568383 Solving 0.9166666665 + x = 1.356568383 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 = 1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.356568383 + -0.9166666665 x = 1.356568383 + -0.9166666665 Combine like terms: 1.356568383 + -0.9166666665 = 0.4399017165 x = 0.4399017165 Simplifying x = 0.4399017165Subproblem 2
x + 0.9166666665 = -1.356568383 Simplifying x + 0.9166666665 = -1.356568383 Reorder the terms: 0.9166666665 + x = -1.356568383 Solving 0.9166666665 + x = -1.356568383 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 = -1.356568383 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.356568383 + -0.9166666665 x = -1.356568383 + -0.9166666665 Combine like terms: -1.356568383 + -0.9166666665 = -2.2732350495 x = -2.2732350495 Simplifying x = -2.2732350495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4399017165, -2.2732350495}
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