Solve x^2-5x+a-2=0

$$x ^ { 2 } - 5 x + a - 2 = 0$$

Solve for a

$$a=2+5x-x^{2}$$

Solution Steps

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

$$-5x+a-2=-x^{2}$$

Add 5x to both sides.

$$a-2=-x^{2}+5x$$

Add 2 to both sides.

$$a=-x^{2}+5x+2$$

Solve for x (complex solution)

$$x=\frac{\sqrt{33-4a}+5}{2}$$

$$x=\frac{-\sqrt{33-4a}+5}{2}$$

Solve for x

$$x=\frac{\sqrt{33-4a}+5}{2}$$

$$x=\frac{-\sqrt{33-4a}+5}{2}\text{, }a\leq \frac{33}{4}$$