Solve for c
c=\left(y+1\right)^{2}-x^{2}-2x
Solve for x (complex solution)
x=\sqrt{y^{2}+2y-c+2}-1
x=-\sqrt{y^{2}+2y-c+2}-1
Solve for x
x=\sqrt{y^{2}+2y-c+2}-1
x=-\sqrt{y^{2}+2y-c+2}-1\text{, }c\leq y^{2}+2y+2
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x^{2}+2x+c=y^{2}+2y+1
Swap sides so that all variable terms are on the left hand side.
2x+c=y^{2}+2y+1-x^{2}
Subtract x^{2} from both sides.
c=y^{2}+2y+1-x^{2}-2x
Subtract 2x from both sides.
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