Solve X^2+y^2=25y^3+x

$$X ^ { 2 } + y ^ { 2 } = 25 y ^ { 3 } + x$$

Solve for x

$$x=X^{2}+y^{2}-25y^{3}$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$25y^{3}+x=X^{2}+y^{2}$$

Subtract 25y^{3} from both sides.

$$x=X^{2}+y^{2}-25y^{3}$$

Solve for X (complex solution)

$$X=-\sqrt{x+25y^{3}-y^{2}}$$

$$X=\sqrt{x+25y^{3}-y^{2}}$$

Solve for X

$$X=\sqrt{x+25y^{3}-y^{2}}$$

$$X=-\sqrt{x+25y^{3}-y^{2}}\text{, }x\geq y^{2}-25y^{3}$$