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Simplifying (2x + -1)(3x + -4) = 5 Reorder the terms: (-1 + 2x)(3x + -4) = 5 Reorder the terms: (-1 + 2x)(-4 + 3x) = 5 Multiply (-1 + 2x) * (-4 + 3x) (-1(-4 + 3x) + 2x * (-4 + 3x)) = 5 ((-4 * -1 + 3x * -1) + 2x * (-4 + 3x)) = 5 ((4 + -3x) + 2x * (-4 + 3x)) = 5 (4 + -3x + (-4 * 2x + 3x * 2x)) = 5 (4 + -3x + (-8x + 6x2)) = 5 Combine like terms: -3x + -8x = -11x (4 + -11x + 6x2) = 5 Solving 4 + -11x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: 4 + -5 + -11x + 6x2 = 5 + -5 Combine like terms: 4 + -5 = -1 -1 + -11x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -1 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.833333333x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.833333333x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + 0.1666666667 -1.833333333x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.833333333x + x2 = 0.1666666667 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 = 0.1666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.1666666667 + 0.8402777775 Combine like terms: 0.1666666667 + 0.8402777775 = 1.0069444442 0.8402777775 + -1.833333333x + x2 = 1.0069444442 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 1.0069444442 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.003466215 and -1.003466215.Subproblem 1
x + -0.9166666665 = 1.003466215 Simplifying x + -0.9166666665 = 1.003466215 Reorder the terms: -0.9166666665 + x = 1.003466215 Solving -0.9166666665 + x = 1.003466215 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 = 1.003466215 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.003466215 + 0.9166666665 x = 1.003466215 + 0.9166666665 Combine like terms: 1.003466215 + 0.9166666665 = 1.9201328815 x = 1.9201328815 Simplifying x = 1.9201328815Subproblem 2
x + -0.9166666665 = -1.003466215 Simplifying x + -0.9166666665 = -1.003466215 Reorder the terms: -0.9166666665 + x = -1.003466215 Solving -0.9166666665 + x = -1.003466215 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 = -1.003466215 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.003466215 + 0.9166666665 x = -1.003466215 + 0.9166666665 Combine like terms: -1.003466215 + 0.9166666665 = -0.0867995485 x = -0.0867995485 Simplifying x = -0.0867995485Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9201328815, -0.0867995485}
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