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There is no integral solution, because none of the factor pairs of 16 add to 6.
x +y = -16
x * y = 6
x (-16 - x) = 6
- x2 - 16 x - 6 = 0
x2 + 16 x + 6 = 0
Quadratically, x and y are the two roots: (-8) + (sq rt 58) and (-8) - (sq rt 58)
Check: (-8 +sq rt 58)*(-8 -sq rt 58) = 6 and (-8 +sq rt 58)+(-8 -sq rt 58) = -16
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