Solve y=x^2+(x^2)^2(y+2)

$$y = x ^ { 2 } + ( x ^ { 2 } ) ^ { 2 } ( y + 2 )$$

Solve for y (complex solution)

$$y=\frac{x^{2}\left(2x^{2}+1\right)}{1-x^{4}}$$

$$x\neq -1\text{ and }x\neq i\text{ and }x\neq -i\text{ and }x\neq 1$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$y=x^{2}+x^{4}\left(y+2\right)$$

Use the distributive property to multiply x^{4} by y+2.

$$y=x^{2}+x^{4}y+2x^{4}$$

Subtract x^{4}y from both sides.

$$y-x^{4}y=x^{2}+2x^{4}$$

Reorder the terms.

$$-yx^{4}+y=2x^{4}+x^{2}$$

Combine all terms containing y.

$$\left(-x^{4}+1\right)y=2x^{4}+x^{2}$$

The equation is in standard form.

$$\left(1-x^{4}\right)y=2x^{4}+x^{2}$$

Divide both sides by 1-x^{4}.

$$\frac{\left(1-x^{4}\right)y}{1-x^{4}}=\frac{2x^{4}+x^{2}}{1-x^{4}}$$

Dividing by 1-x^{4} undoes the multiplication by 1-x^{4}.

$$y=\frac{2x^{4}+x^{2}}{1-x^{4}}$$

Divide 2x^{4}+x^{2} by 1-x^{4}.

$$y=\frac{x^{2}\left(2x^{2}+1\right)}{1-x^{4}}$$

Solve for y

$$y=\frac{x^{2}\left(2x^{2}+1\right)}{1-x^{4}}$$

$$|x|\neq 1$$

Steps for Solving Linear Equation

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$y=x^{2}+x^{4}\left(y+2\right)$$

Use the distributive property to multiply x^{4} by y+2.

$$y=x^{2}+x^{4}y+2x^{4}$$

Subtract x^{4}y from both sides.

$$y-x^{4}y=x^{2}+2x^{4}$$

Reorder the terms.

$$-yx^{4}+y=2x^{4}+x^{2}$$

Combine all terms containing y.

$$\left(-x^{4}+1\right)y=2x^{4}+x^{2}$$

The equation is in standard form.

$$\left(1-x^{4}\right)y=2x^{4}+x^{2}$$

Divide both sides by 1-x^{4}.

$$\frac{\left(1-x^{4}\right)y}{1-x^{4}}=\frac{2x^{4}+x^{2}}{1-x^{4}}$$

Dividing by 1-x^{4} undoes the multiplication by 1-x^{4}.

$$y=\frac{2x^{4}+x^{2}}{1-x^{4}}$$

Divide 2x^{4}+x^{2} by 1-x^{4}.

$$y=\frac{x^{2}\left(2x^{2}+1\right)}{1-x^{4}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{i\left(y+2\right)^{-\frac{1}{2}}\sqrt{2\sqrt{4y^{2}+8y+1}+2}}{2}\text{; }x=-\frac{i\left(y+2\right)^{-\frac{1}{2}}\sqrt{2\sqrt{4y^{2}+8y+1}+2}}{2}\text{; }x=-\frac{i\left(y+2\right)^{-\frac{1}{2}}\sqrt{-2\sqrt{4y^{2}+8y+1}+2}}{2}\text{; }x=\frac{i\left(y+2\right)^{-\frac{1}{2}}\sqrt{-2\sqrt{4y^{2}+8y+1}+2}}{2}\text{, }&y\neq -2\\x=-\sqrt{2}i\approx -0-1.414213562i\text{; }x=\sqrt{2}i\approx 1.414213562i\text{, }&y=-2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{\frac{2\left(\sqrt{4y^{2}+8y+1}-1\right)}{y+2}}}{2}\text{; }x=\frac{\sqrt{\frac{2\left(\sqrt{4y^{2}+8y+1}-1\right)}{y+2}}}{2}\text{, }&y\geq 0\\x=-\frac{\sqrt{-\frac{2\left(\sqrt{4y^{2}+8y+1}+1\right)}{y+2}}}{2}\text{; }x=\frac{\sqrt{-\frac{2\left(\sqrt{4y^{2}+8y+1}+1\right)}{y+2}}}{2}\text{, }&y<-2\end{matrix}\right.$$