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Simplifying 0 = (5x + 2y + 1)(25x2 + -10xy + 4y2 + 1) Reorder the terms: 0 = (1 + 5x + 2y)(25x2 + -10xy + 4y2 + 1) Reorder the terms: 0 = (1 + 5x + 2y)(1 + -10xy + 25x2 + 4y2) Multiply (1 + 5x + 2y) * (1 + -10xy + 25x2 + 4y2) 0 = (1(1 + -10xy + 25x2 + 4y2) + 5x * (1 + -10xy + 25x2 + 4y2) + 2y * (1 + -10xy + 25x2 + 4y2)) 0 = ((1 * 1 + -10xy * 1 + 25x2 * 1 + 4y2 * 1) + 5x * (1 + -10xy + 25x2 + 4y2) + 2y * (1 + -10xy + 25x2 + 4y2)) 0 = ((1 + -10xy + 25x2 + 4y2) + 5x * (1 + -10xy + 25x2 + 4y2) + 2y * (1 + -10xy + 25x2 + 4y2)) 0 = (1 + -10xy + 25x2 + 4y2 + (1 * 5x + -10xy * 5x + 25x2 * 5x + 4y2 * 5x) + 2y * (1 + -10xy + 25x2 + 4y2)) Reorder the terms: 0 = (1 + -10xy + 25x2 + 4y2 + (5x + 20xy2 + -50x2y + 125x3) + 2y * (1 + -10xy + 25x2 + 4y2)) 0 = (1 + -10xy + 25x2 + 4y2 + (5x + 20xy2 + -50x2y + 125x3) + 2y * (1 + -10xy + 25x2 + 4y2)) 0 = (1 + -10xy + 25x2 + 4y2 + 5x + 20xy2 + -50x2y + 125x3 + (1 * 2y + -10xy * 2y + 25x2 * 2y + 4y2 * 2y)) Reorder the terms: 0 = (1 + -10xy + 25x2 + 4y2 + 5x + 20xy2 + -50x2y + 125x3 + (-20xy2 + 50x2y + 2y + 8y3)) 0 = (1 + -10xy + 25x2 + 4y2 + 5x + 20xy2 + -50x2y + 125x3 + (-20xy2 + 50x2y + 2y + 8y3)) Reorder the terms: 0 = (1 + 5x + -10xy + 20xy2 + -20xy2 + 25x2 + -50x2y + 50x2y + 125x3 + 2y + 4y2 + 8y3) Combine like terms: 20xy2 + -20xy2 = 0 0 = (1 + 5x + -10xy + 0 + 25x2 + -50x2y + 50x2y + 125x3 + 2y + 4y2 + 8y3) 0 = (1 + 5x + -10xy + 25x2 + -50x2y + 50x2y + 125x3 + 2y + 4y2 + 8y3) Combine like terms: -50x2y + 50x2y = 0 0 = (1 + 5x + -10xy + 25x2 + 0 + 125x3 + 2y + 4y2 + 8y3) 0 = (1 + 5x + -10xy + 25x2 + 125x3 + 2y + 4y2 + 8y3) Solving 0 = 1 + 5x + -10xy + 25x2 + 125x3 + 2y + 4y2 + 8y3 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 1 + 5x + -10xy + 25x2 + 125x3 + 2y + 4y2 + 8y3 + -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 Reorder the terms: -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 1 + -1 + 5x + -5x + -10xy + 10xy + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 1 + -1 = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 5x + -5x + -10xy + 10xy + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 5x + -5x + -10xy + 10xy + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 5x + -5x = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + -10xy + 10xy + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = -10xy + 10xy + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: -10xy + 10xy = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 25x2 + -25x2 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 25x2 + -25x2 = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 125x3 + -125x3 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 125x3 + -125x3 = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 2y + -2y + 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 2y + -2y = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 4y2 + -4y2 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 4y2 + -4y2 + 8y3 + -8y3 Combine like terms: 4y2 + -4y2 = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 + 8y3 + -8y3 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 8y3 + -8y3 Combine like terms: 8y3 + -8y3 = 0 -1 + -5x + 10xy + -25x2 + -125x3 + -2y + -4y2 + -8y3 = 0 The solution to this equation could not be determined.
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