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

Question

2592 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-03T19:20:54

$-x^2+15x-50 = 0$
or, equivalnetly
$(-1)(x^2-15x+50) = 0$

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

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

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

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).

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