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Simplifying X3 + 3X + -2 = X3 + X2 + X + 1 Reorder the terms: -2 + 3X + X3 = X3 + X2 + X + 1 Reorder the terms: -2 + 3X + X3 = 1 + X + X2 + X3 Add '-1X3' to each side of the equation. -2 + 3X + X3 + -1X3 = 1 + X + X2 + X3 + -1X3 Combine like terms: X3 + -1X3 = 0 -2 + 3X + 0 = 1 + X + X2 + X3 + -1X3 -2 + 3X = 1 + X + X2 + X3 + -1X3 Combine like terms: X3 + -1X3 = 0 -2 + 3X = 1 + X + X2 + 0 -2 + 3X = 1 + X + X2 Solving -2 + 3X = 1 + X + X2 Solving for variable 'X'. Reorder the terms: -2 + -1 + 3X + -1X + -1X2 = 1 + X + X2 + -1 + -1X + -1X2 Combine like terms: -2 + -1 = -3 -3 + 3X + -1X + -1X2 = 1 + X + X2 + -1 + -1X + -1X2 Combine like terms: 3X + -1X = 2X -3 + 2X + -1X2 = 1 + X + X2 + -1 + -1X + -1X2 Reorder the terms: -3 + 2X + -1X2 = 1 + -1 + X + -1X + X2 + -1X2 Combine like terms: 1 + -1 = 0 -3 + 2X + -1X2 = 0 + X + -1X + X2 + -1X2 -3 + 2X + -1X2 = X + -1X + X2 + -1X2 Combine like terms: X + -1X = 0 -3 + 2X + -1X2 = 0 + X2 + -1X2 -3 + 2X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -3 + 2X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -2X + X2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + -2X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2X + X2 = 0 + -3 -2X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2X + X2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2X + X2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2X + X2 = -2 Factor a perfect square on the left side: (X + -1)(X + -1) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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