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Simplifying (4x + 1)(3x + -1) + (2x + -5) * 2 = (8x + 1)(2x + -1) Reorder the terms: (1 + 4x)(3x + -1) + (2x + -5) * 2 = (8x + 1)(2x + -1) Reorder the terms: (1 + 4x)(-1 + 3x) + (2x + -5) * 2 = (8x + 1)(2x + -1) Multiply (1 + 4x) * (-1 + 3x) (1(-1 + 3x) + 4x * (-1 + 3x)) + (2x + -5) * 2 = (8x + 1)(2x + -1) ((-1 * 1 + 3x * 1) + 4x * (-1 + 3x)) + (2x + -5) * 2 = (8x + 1)(2x + -1) ((-1 + 3x) + 4x * (-1 + 3x)) + (2x + -5) * 2 = (8x + 1)(2x + -1) (-1 + 3x + (-1 * 4x + 3x * 4x)) + (2x + -5) * 2 = (8x + 1)(2x + -1) (-1 + 3x + (-4x + 12x2)) + (2x + -5) * 2 = (8x + 1)(2x + -1) Combine like terms: 3x + -4x = -1x (-1 + -1x + 12x2) + (2x + -5) * 2 = (8x + 1)(2x + -1) Reorder the terms: -1 + -1x + 12x2 + (-5 + 2x) * 2 = (8x + 1)(2x + -1) Reorder the terms for easier multiplication: -1 + -1x + 12x2 + 2(-5 + 2x) = (8x + 1)(2x + -1) -1 + -1x + 12x2 + (-5 * 2 + 2x * 2) = (8x + 1)(2x + -1) -1 + -1x + 12x2 + (-10 + 4x) = (8x + 1)(2x + -1) Reorder the terms: -1 + -10 + -1x + 4x + 12x2 = (8x + 1)(2x + -1) Combine like terms: -1 + -10 = -11 -11 + -1x + 4x + 12x2 = (8x + 1)(2x + -1) Combine like terms: -1x + 4x = 3x -11 + 3x + 12x2 = (8x + 1)(2x + -1) Reorder the terms: -11 + 3x + 12x2 = (1 + 8x)(2x + -1) Reorder the terms: -11 + 3x + 12x2 = (1 + 8x)(-1 + 2x) Multiply (1 + 8x) * (-1 + 2x) -11 + 3x + 12x2 = (1(-1 + 2x) + 8x * (-1 + 2x)) -11 + 3x + 12x2 = ((-1 * 1 + 2x * 1) + 8x * (-1 + 2x)) -11 + 3x + 12x2 = ((-1 + 2x) + 8x * (-1 + 2x)) -11 + 3x + 12x2 = (-1 + 2x + (-1 * 8x + 2x * 8x)) -11 + 3x + 12x2 = (-1 + 2x + (-8x + 16x2)) Combine like terms: 2x + -8x = -6x -11 + 3x + 12x2 = (-1 + -6x + 16x2) Solving -11 + 3x + 12x2 = -1 + -6x + 16x2 Solving for variable 'x'. Reorder the terms: -11 + 1 + 3x + 6x + 12x2 + -16x2 = -1 + -6x + 16x2 + 1 + 6x + -16x2 Combine like terms: -11 + 1 = -10 -10 + 3x + 6x + 12x2 + -16x2 = -1 + -6x + 16x2 + 1 + 6x + -16x2 Combine like terms: 3x + 6x = 9x -10 + 9x + 12x2 + -16x2 = -1 + -6x + 16x2 + 1 + 6x + -16x2 Combine like terms: 12x2 + -16x2 = -4x2 -10 + 9x + -4x2 = -1 + -6x + 16x2 + 1 + 6x + -16x2 Reorder the terms: -10 + 9x + -4x2 = -1 + 1 + -6x + 6x + 16x2 + -16x2 Combine like terms: -1 + 1 = 0 -10 + 9x + -4x2 = 0 + -6x + 6x + 16x2 + -16x2 -10 + 9x + -4x2 = -6x + 6x + 16x2 + -16x2 Combine like terms: -6x + 6x = 0 -10 + 9x + -4x2 = 0 + 16x2 + -16x2 -10 + 9x + -4x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -10 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.5 + -2.25x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2.25x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2.25x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.25x + x2 = 0 + -2.5 -2.25x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2.25x + x2 = -2.5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -2.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -2.5 + 1.265625 Combine like terms: -2.5 + 1.265625 = -1.234375 1.265625 + -2.25x + x2 = -1.234375 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = -1.234375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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