Solve x^2-13x+k=0

$$x ^ { 2 } - 13 x + k = 0$$

Solve for k

$$k=-x\left(x-13\right)$$

Solution Steps

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

$$-13x+k=-x^{2}$$

Add 13x to both sides.

$$k=-x^{2}+13x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{169-4k}+13}{2}$$

$$x=\frac{-\sqrt{169-4k}+13}{2}$$

Solve for x

$$x=\frac{\sqrt{169-4k}+13}{2}$$

$$x=\frac{-\sqrt{169-4k}+13}{2}\text{, }k\leq \frac{169}{4}$$