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Simplifying (4x + -3)(x + -5) = (-11x + 1)(3x + -2) Reorder the terms: (-3 + 4x)(x + -5) = (-11x + 1)(3x + -2) Reorder the terms: (-3 + 4x)(-5 + x) = (-11x + 1)(3x + -2) Multiply (-3 + 4x) * (-5 + x) (-3(-5 + x) + 4x * (-5 + x)) = (-11x + 1)(3x + -2) ((-5 * -3 + x * -3) + 4x * (-5 + x)) = (-11x + 1)(3x + -2) ((15 + -3x) + 4x * (-5 + x)) = (-11x + 1)(3x + -2) (15 + -3x + (-5 * 4x + x * 4x)) = (-11x + 1)(3x + -2) (15 + -3x + (-20x + 4x2)) = (-11x + 1)(3x + -2) Combine like terms: -3x + -20x = -23x (15 + -23x + 4x2) = (-11x + 1)(3x + -2) Reorder the terms: 15 + -23x + 4x2 = (1 + -11x)(3x + -2) Reorder the terms: 15 + -23x + 4x2 = (1 + -11x)(-2 + 3x) Multiply (1 + -11x) * (-2 + 3x) 15 + -23x + 4x2 = (1(-2 + 3x) + -11x * (-2 + 3x)) 15 + -23x + 4x2 = ((-2 * 1 + 3x * 1) + -11x * (-2 + 3x)) 15 + -23x + 4x2 = ((-2 + 3x) + -11x * (-2 + 3x)) 15 + -23x + 4x2 = (-2 + 3x + (-2 * -11x + 3x * -11x)) 15 + -23x + 4x2 = (-2 + 3x + (22x + -33x2)) Combine like terms: 3x + 22x = 25x 15 + -23x + 4x2 = (-2 + 25x + -33x2) Solving 15 + -23x + 4x2 = -2 + 25x + -33x2 Solving for variable 'x'. Reorder the terms: 15 + 2 + -23x + -25x + 4x2 + 33x2 = -2 + 25x + -33x2 + 2 + -25x + 33x2 Combine like terms: 15 + 2 = 17 17 + -23x + -25x + 4x2 + 33x2 = -2 + 25x + -33x2 + 2 + -25x + 33x2 Combine like terms: -23x + -25x = -48x 17 + -48x + 4x2 + 33x2 = -2 + 25x + -33x2 + 2 + -25x + 33x2 Combine like terms: 4x2 + 33x2 = 37x2 17 + -48x + 37x2 = -2 + 25x + -33x2 + 2 + -25x + 33x2 Reorder the terms: 17 + -48x + 37x2 = -2 + 2 + 25x + -25x + -33x2 + 33x2 Combine like terms: -2 + 2 = 0 17 + -48x + 37x2 = 0 + 25x + -25x + -33x2 + 33x2 17 + -48x + 37x2 = 25x + -25x + -33x2 + 33x2 Combine like terms: 25x + -25x = 0 17 + -48x + 37x2 = 0 + -33x2 + 33x2 17 + -48x + 37x2 = -33x2 + 33x2 Combine like terms: -33x2 + 33x2 = 0 17 + -48x + 37x2 = 0 Begin completing the square. Divide all terms by 37 the coefficient of the squared term: Divide each side by '37'. 0.4594594595 + -1.297297297x + x2 = 0 Move the constant term to the right: Add '-0.4594594595' to each side of the equation. 0.4594594595 + -1.297297297x + -0.4594594595 + x2 = 0 + -0.4594594595 Reorder the terms: 0.4594594595 + -0.4594594595 + -1.297297297x + x2 = 0 + -0.4594594595 Combine like terms: 0.4594594595 + -0.4594594595 = 0.0000000000 0.0000000000 + -1.297297297x + x2 = 0 + -0.4594594595 -1.297297297x + x2 = 0 + -0.4594594595 Combine like terms: 0 + -0.4594594595 = -0.4594594595 -1.297297297x + x2 = -0.4594594595 The x term is -1.297297297x. Take half its coefficient (-0.6486486485). Square it (0.4207450692) and add it to both sides. Add '0.4207450692' to each side of the equation. -1.297297297x + 0.4207450692 + x2 = -0.4594594595 + 0.4207450692 Reorder the terms: 0.4207450692 + -1.297297297x + x2 = -0.4594594595 + 0.4207450692 Combine like terms: -0.4594594595 + 0.4207450692 = -0.0387143903 0.4207450692 + -1.297297297x + x2 = -0.0387143903 Factor a perfect square on the left side: (x + -0.6486486485)(x + -0.6486486485) = -0.0387143903 Can't calculate square root of the right side. The solution to this equation could not be determined.
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