Solve x^2+(y-2^3)(x^2)^2=0

$$x ^ { 2 } + ( y - 2 ^ { 3 } ) ( x ^ { 2 } ) ^ { 2 } = 0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=8-\frac{1}{x^{2}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+\left(y-2^{3}\right)x^{4}=0$$

Calculate 2 to the power of 3 and get 8.

$$x^{2}+\left(y-8\right)x^{4}=0$$

Use the distributive property to multiply y-8 by x^{4}.

$$x^{2}+yx^{4}-8x^{4}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$yx^{4}-8x^{4}=-x^{2}$$

Add 8x^{4} to both sides.

$$yx^{4}=-x^{2}+8x^{4}$$

The equation is in standard form.

$$x^{4}y=8x^{4}-x^{2}$$

Divide both sides by x^{4}.

$$\frac{x^{4}y}{x^{4}}=\frac{x^{2}\left(8x^{2}-1\right)}{x^{4}}$$

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

$$y=\frac{x^{2}\left(8x^{2}-1\right)}{x^{4}}$$

Divide \left(-1+8x^{2}\right)x^{2} by x^{4}.

$$y=8-\frac{1}{x^{2}}$$

Solve for y

$$\left\{\begin{matrix}y=8-\frac{1}{x^{2}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x^{2}+\left(y-2^{3}\right)x^{4}=0$$

Calculate 2 to the power of 3 and get 8.

$$x^{2}+\left(y-8\right)x^{4}=0$$

Use the distributive property to multiply y-8 by x^{4}.

$$x^{2}+yx^{4}-8x^{4}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$yx^{4}-8x^{4}=-x^{2}$$

Add 8x^{4} to both sides.

$$yx^{4}=-x^{2}+8x^{4}$$

The equation is in standard form.

$$x^{4}y=8x^{4}-x^{2}$$

Divide both sides by x^{4}.

$$\frac{x^{4}y}{x^{4}}=\frac{x^{2}\left(8x^{2}-1\right)}{x^{4}}$$

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

$$y=\frac{x^{2}\left(8x^{2}-1\right)}{x^{4}}$$

Divide \left(-1+8x^{2}\right)x^{2} by x^{4}.

$$y=8-\frac{1}{x^{2}}$$

Solve for x (complex solution)

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

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{-\frac{1}{y-8}}\text{; }x=-\sqrt{-\frac{1}{y-8}}\text{, }&y<8\end{matrix}\right.$$