Answer
$-5$
Work Step by Step
$x-(1/x)=-24/5$
$x<0$
$x-(1/x)=-24/5$
$x-(1/x)=-24/5$
$x*(x-(1/x))=-24/5*x$
$x^2-1=-24x/5$
$5*(x^2-1)=-24x/5*5$
$5x^2-5=-24x$
$5x^2-5+24x=-24x+24x$
$5x^2+24x-5=0$
$a=5$, $b=24$, $c=-5$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-24±\sqrt {24^2-4*5*(-5)})/2*5$
$x=(-24±\sqrt {576+100})/10$
$x=(-24±\sqrt {676})/10$
$x=(-24±26)/10$
$x=(-24±26)/10$
$x=(-24+26)/10$
$x=2/10$
$x=1/5$
This answer is not valid since we were looking for a negative number.
$x=(-24±26)/10$
$x=(-24-26)/10$
$x=-50/10$
$x=-5$
$-5-(-1/5)$
$-25/5 - (-1/5)$
$-25/5 + 1/5$
$-24/5$
