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

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

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Answer 1 · 2015-05-03T19:20:54

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

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

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

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

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

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

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