Solve y=x^2-4x-k

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

Solve for k

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

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

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

Add 4x to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for x (complex solution)

$$x=\sqrt{y+k+4}+2$$

$$x=-\sqrt{y+k+4}+2$$

Solve for x

$$x=\sqrt{y+k+4}+2$$

$$x=-\sqrt{y+k+4}+2\text{, }y\geq -\left(k+4\right)$$