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Simplifying 0 = X2 + -2X + 1000 Reorder the terms: 0 = 1000 + -2X + X2 Solving 0 = 1000 + -2X + X2 Solving for variable 'X'. Combine like terms: 0 + -1000 = -1000 -1000 + 2X + -1X2 = 1000 + -2X + X2 + -1000 + 2X + -1X2 Reorder the terms: -1000 + 2X + -1X2 = 1000 + -1000 + -2X + 2X + X2 + -1X2 Combine like terms: 1000 + -1000 = 0 -1000 + 2X + -1X2 = 0 + -2X + 2X + X2 + -1X2 -1000 + 2X + -1X2 = -2X + 2X + X2 + -1X2 Combine like terms: -2X + 2X = 0 -1000 + 2X + -1X2 = 0 + X2 + -1X2 -1000 + 2X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -1000 + 2X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1000 + -2X + X2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -2X + -1000 + X2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -2X + X2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -2X + X2 = 0 + -1000 -2X + X2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -2X + X2 = -1000 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = -1000 + 1 Reorder the terms: 1 + -2X + X2 = -1000 + 1 Combine like terms: -1000 + 1 = -999 1 + -2X + X2 = -999 Factor a perfect square on the left side: (X + -1)(X + -1) = -999 Can't calculate square root of the right side. The solution to this equation could not be determined.
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