Solve for x
x=-\left(y^{2}+6\right)
Solve for y (complex solution)
y=-i\sqrt{x+6}
y=i\sqrt{x+6}
Solve for y
y=\sqrt{-x-6}
y=-\sqrt{-x-6}\text{, }x\leq -6
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x+6=-y^{2}
Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.
x=-y^{2}-6
Subtract 6 from both sides.
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