# How do you solve x^2 - 3x - 10 = 0 ?

Jun 14, 2015

${x}^{2} - 3 x - 10 = \left(x - 5\right) \left(x + 2\right)$

So ${x}^{2} - 3 x - 10 = 0$ has roots $x = 5$ and $x = - 2$.

#### Explanation:

If ${x}^{2} - 3 x - 10 = \left(x - a\right) \left(x + b\right) = {x}^{2} - \left(a - b\right) x - a b$

then $a \cdot b = 10$ and $a - b = 3$.

That is satisfied by $a = 5$ and $b = 2$.