# How do you solve x^2=13x-42?

Dec 27, 2015

The roots of $x$ are $7$ and $6$

#### Explanation:

This equation may be written as

${x}^{2} - 13 x + 42 = 0$

or

${x}^{2} - 7 x - 6 x + 42 = 0$

or

$x \left(x - 7\right) - 6 \left(x - 7\right) = 0$

or

$\left(x - 7\right) \left(x - 6\right) = 0$

So $x - 7 = 0$ or $x - 6 = 0$

therefore $x = 7$ or $6$