# How do you factor -x^2+15x-50=0?

##### 1 Answer
May 3, 2015

$- {x}^{2} + 15 x - 50 = 0$
or, equivalnetly
$\left(- 1\right) \left({x}^{2} - 15 x + 50\right) = 0$

We are looking for two constants: $a$ and $b$ such that
$a + b = - 15$
and
$a \times b = 50$

The obvious pair is $\left(a , b\right) = \left(- 5 , - 10\right)$
gives us
$- {x}^{2} + 15 x - 50 = 0$
$\equiv \left(- 1\right) \left(x - 5\right) \left(x - 10\right) = 0$

Note that it is unusual to be asked to factor an equation; normally we only factor expressions:
$- {x}^{2} + 15 x - 50 = \left(- 1\right) \left(x - 5\right) \left(x - 10\right)$

It may be that the intent was to extract
$x - 5 = 0$
and
$x - 10 = 0$
as factors of the original equation (check with your instructor).