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Simplifying (2x + 1)(3x + -2) = (x + -5)(2x + 3) Reorder the terms: (1 + 2x)(3x + -2) = (x + -5)(2x + 3) Reorder the terms: (1 + 2x)(-2 + 3x) = (x + -5)(2x + 3) Multiply (1 + 2x) * (-2 + 3x) (1(-2 + 3x) + 2x * (-2 + 3x)) = (x + -5)(2x + 3) ((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) = (x + -5)(2x + 3) ((-2 + 3x) + 2x * (-2 + 3x)) = (x + -5)(2x + 3) (-2 + 3x + (-2 * 2x + 3x * 2x)) = (x + -5)(2x + 3) (-2 + 3x + (-4x + 6x2)) = (x + -5)(2x + 3) Combine like terms: 3x + -4x = -1x (-2 + -1x + 6x2) = (x + -5)(2x + 3) Reorder the terms: -2 + -1x + 6x2 = (-5 + x)(2x + 3) Reorder the terms: -2 + -1x + 6x2 = (-5 + x)(3 + 2x) Multiply (-5 + x) * (3 + 2x) -2 + -1x + 6x2 = (-5(3 + 2x) + x(3 + 2x)) -2 + -1x + 6x2 = ((3 * -5 + 2x * -5) + x(3 + 2x)) -2 + -1x + 6x2 = ((-15 + -10x) + x(3 + 2x)) -2 + -1x + 6x2 = (-15 + -10x + (3 * x + 2x * x)) -2 + -1x + 6x2 = (-15 + -10x + (3x + 2x2)) Combine like terms: -10x + 3x = -7x -2 + -1x + 6x2 = (-15 + -7x + 2x2) Solving -2 + -1x + 6x2 = -15 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -2 + 15 + -1x + 7x + 6x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: -2 + 15 = 13 13 + -1x + 7x + 6x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: -1x + 7x = 6x 13 + 6x + 6x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 13 + 6x + 4x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Reorder the terms: 13 + 6x + 4x2 = -15 + 15 + -7x + 7x + 2x2 + -2x2 Combine like terms: -15 + 15 = 0 13 + 6x + 4x2 = 0 + -7x + 7x + 2x2 + -2x2 13 + 6x + 4x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 13 + 6x + 4x2 = 0 + 2x2 + -2x2 13 + 6x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 13 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 1.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 1.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 1.5x + x2 = 0 + -3.25 1.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 1.5x + x2 = -3.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -3.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.25 + 0.5625 Combine like terms: -3.25 + 0.5625 = -2.6875 0.5625 + 1.5x + x2 = -2.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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