Solve f(x)=-x^2+4quady(x)=x^2

$$f ( x ) = - x ^ { 2 } + 4 \quad y ( x ) = x ^ { 2 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{x}{2}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

The equation is in standard form.

$$4xy=2x^{2}$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{2x^{2}}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{2x^{2}}{4x}$$

Divide 2x^{2} by 4x.

$$y=\frac{x}{2}$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{x}{2}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

The equation is in standard form.

$$4xy=2x^{2}$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{2x^{2}}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{2x^{2}}{4x}$$

Divide 2x^{2} by 4x.

$$y=\frac{x}{2}$$

Solve for x

$$x=2y$$

$$x=0$$