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Simplifying -256 = (X + -32)(X + -32) Reorder the terms: -256 = (-32 + X)(X + -32) Reorder the terms: -256 = (-32 + X)(-32 + X) Multiply (-32 + X) * (-32 + X) -256 = (-32(-32 + X) + X(-32 + X)) -256 = ((-32 * -32 + X * -32) + X(-32 + X)) -256 = ((1024 + -32X) + X(-32 + X)) -256 = (1024 + -32X + (-32 * X + X * X)) -256 = (1024 + -32X + (-32X + X2)) Combine like terms: -32X + -32X = -64X -256 = (1024 + -64X + X2) Solving -256 = 1024 + -64X + X2 Solving for variable 'X'. Combine like terms: -256 + -1024 = -1280 -1280 + 64X + -1X2 = 1024 + -64X + X2 + -1024 + 64X + -1X2 Reorder the terms: -1280 + 64X + -1X2 = 1024 + -1024 + -64X + 64X + X2 + -1X2 Combine like terms: 1024 + -1024 = 0 -1280 + 64X + -1X2 = 0 + -64X + 64X + X2 + -1X2 -1280 + 64X + -1X2 = -64X + 64X + X2 + -1X2 Combine like terms: -64X + 64X = 0 -1280 + 64X + -1X2 = 0 + X2 + -1X2 -1280 + 64X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -1280 + 64X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1280 + -64X + X2 = 0 Move the constant term to the right: Add '-1280' to each side of the equation. 1280 + -64X + -1280 + X2 = 0 + -1280 Reorder the terms: 1280 + -1280 + -64X + X2 = 0 + -1280 Combine like terms: 1280 + -1280 = 0 0 + -64X + X2 = 0 + -1280 -64X + X2 = 0 + -1280 Combine like terms: 0 + -1280 = -1280 -64X + X2 = -1280 The X term is -64X. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64X + 1024 + X2 = -1280 + 1024 Reorder the terms: 1024 + -64X + X2 = -1280 + 1024 Combine like terms: -1280 + 1024 = -256 1024 + -64X + X2 = -256 Factor a perfect square on the left side: (X + -32)(X + -32) = -256 Can't calculate square root of the right side. The solution to this equation could not be determined.
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