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Simplifying 0 = -0.5x2 + 25x + -1350 Reorder the terms: 0 = -1350 + 25x + -0.5x2 Solving 0 = -1350 + 25x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 1350 = 1350 1350 + -25x + 0.5x2 = -1350 + 25x + -0.5x2 + 1350 + -25x + 0.5x2 Reorder the terms: 1350 + -25x + 0.5x2 = -1350 + 1350 + 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: -1350 + 1350 = 0 1350 + -25x + 0.5x2 = 0 + 25x + -25x + -0.5x2 + 0.5x2 1350 + -25x + 0.5x2 = 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: 25x + -25x = 0 1350 + -25x + 0.5x2 = 0 + -0.5x2 + 0.5x2 1350 + -25x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 1350 + -25x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 2700 + -50x + x2 = 0 Move the constant term to the right: Add '-2700' to each side of the equation. 2700 + -50x + -2700 + x2 = 0 + -2700 Reorder the terms: 2700 + -2700 + -50x + x2 = 0 + -2700 Combine like terms: 2700 + -2700 = 0 0 + -50x + x2 = 0 + -2700 -50x + x2 = 0 + -2700 Combine like terms: 0 + -2700 = -2700 -50x + x2 = -2700 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -2700 + 625 Reorder the terms: 625 + -50x + x2 = -2700 + 625 Combine like terms: -2700 + 625 = -2075 625 + -50x + x2 = -2075 Factor a perfect square on the left side: (x + -25)(x + -25) = -2075 Can't calculate square root of the right side. The solution to this equation could not be determined.
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