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Simplifying (3 + 5x)(2 + -3x) = 12 + -15x Multiply (3 + 5x) * (2 + -3x) (3(2 + -3x) + 5x * (2 + -3x)) = 12 + -15x ((2 * 3 + -3x * 3) + 5x * (2 + -3x)) = 12 + -15x ((6 + -9x) + 5x * (2 + -3x)) = 12 + -15x (6 + -9x + (2 * 5x + -3x * 5x)) = 12 + -15x (6 + -9x + (10x + -15x2)) = 12 + -15x Combine like terms: -9x + 10x = 1x (6 + 1x + -15x2) = 12 + -15x Solving 6 + 1x + -15x2 = 12 + -15x Solving for variable 'x'. Reorder the terms: 6 + -12 + 1x + 15x + -15x2 = 12 + -15x + -12 + 15x Combine like terms: 6 + -12 = -6 -6 + 1x + 15x + -15x2 = 12 + -15x + -12 + 15x Combine like terms: 1x + 15x = 16x -6 + 16x + -15x2 = 12 + -15x + -12 + 15x Reorder the terms: -6 + 16x + -15x2 = 12 + -12 + -15x + 15x Combine like terms: 12 + -12 = 0 -6 + 16x + -15x2 = 0 + -15x + 15x -6 + 16x + -15x2 = -15x + 15x Combine like terms: -15x + 15x = 0 -6 + 16x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.4 + -1.066666667x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.066666667x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.066666667x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.066666667x + x2 = 0 + -0.4 -1.066666667x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.066666667x + x2 = -0.4 The x term is -1.066666667x. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667x + 0.2844444446 + x2 = -0.4 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667x + x2 = -0.4 + 0.2844444446 Combine like terms: -0.4 + 0.2844444446 = -0.1155555554 0.2844444446 + -1.066666667x + x2 = -0.1155555554 Factor a perfect square on the left side: (x + -0.5333333335)(x + -0.5333333335) = -0.1155555554 Can't calculate square root of the right side. The solution to this equation could not be determined.
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