Question 83952
Start with the given formula

{{{d=sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}


Now plug in the given points (x,5) and (-7,-6) and the distance {{{d=sqrt(146)}}}


{{{sqrt(146)=sqrt((x-(-7))^2+(5-(-6))^2)}}} Plug in the given info


{{{sqrt(146)=sqrt((x+7)^2+(5+6)^2)}}} Subtract the negatives


{{{sqrt(146)=sqrt((x+7)^2+(11)^2)}}} Add


{{{sqrt(146)=sqrt((x+7)^2+121)}}} Square 11


{{{(sqrt(146))^2=(x+7)^2+121}}} Square both sides


{{{146=(x+7)^2+121}}} 


{{{146-121=(x+7)^2}}} Subtract 121 from both sides


{{{25=(x+7)^2}}} Combine like terms


{{{sqrt(25)=x+7}}} Take the square root of both sides


{{{5=x+7}}}


{{{5-7=x}}} Subtract 7 from both sides


{{{x=-2}}} Combine like terms


So the value of x is -2


I'm not sure why the answers are listed in pairs, but I do see a -2 as one of the possible answers.