Solve x^2-4x+(k-1)=0

$$x ^ { 2 } - 4 x + ( k - 1 ) = 0$$

Solve for k

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

Solution Steps

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

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

Add 4x to both sides.

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

Add 1 to both sides.

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

Solve for x (complex solution)

$$x=\sqrt{5-k}+2$$

$$x=-\sqrt{5-k}+2$$

Solve for x

$$x=\sqrt{5-k}+2$$

$$x=-\sqrt{5-k}+2\text{, }k\leq 5$$