Solve x^2-6x+k-1=0

$$x ^ { 2 } - 6 x + k - 1 = 0$$

Solve for k

$$k=1+6x-x^{2}$$

Solution Steps

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

$$-6x+k-1=-x^{2}$$

Add 6x to both sides.

$$k-1=-x^{2}+6x$$

Add 1 to both sides.

$$k=-x^{2}+6x+1$$

Solve for x (complex solution)

$$x=\sqrt{10-k}+3$$

$$x=-\sqrt{10-k}+3$$

Solve for x

$$x=\sqrt{10-k}+3$$

$$x=-\sqrt{10-k}+3\text{, }k\leq 10$$