Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 790: 75

$x=-1/2, 1/3$

$x^{-2}-x^{-1}-6=0$ $1/{x^2}-1/x-6=0$ $1*x^2/{x^2}-1*x^2/x-6*x^2=0*x^2$ $1-x-6x^2=0$ $-6x^2-x+1=0$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-(-1)±\sqrt {(-1)^2-4*(-6)*1})/2(-6)$ $x=(1±\sqrt {1+24})/-12$ $x=(1±\sqrt {25})/-12$ $x=(1±5)/-12$ $x=(1±5)/-12$ $x=(1+5)/-12$ $x=6/-12$ $x=-1/2$ $x=(1±5)/-12$ $x=(1-5)/-12$ $x=-4/-12$ $x=1/3$