Question 98450
Start with the given distance formula

{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} where *[Tex \Large \left(x_{1}, y_{1}\right)] is the first point *[Tex \Large \left(4,-3\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(x,3\right)]


{{{10=sqrt((4-x)^2+(-3-3)^2)}}} Plug in {{{d=10}}},  {{{x[1]=4}}}, {{{x[2]=x}}}, {{{y[1]=-3}}}, {{{y[2]=3}}}



{{{10=sqrt((4-x)^2+(-6)^2)}}} Evaluate {{{-3-3}}} to get -6.



{{{10=sqrt((4-x)^2+36)}}} Square -6 to get 36





{{{100=(4-x)^2+36}}} Square both sides



{{{64=(4-x)^2}}} Subtract 36 from both sides


{{{8=4-x}}} Take the square root of both sides



{{{4=-x}}} Subtract 4 from both sides



{{{-4=x}}} Multiply both sides by -1



So our answer is {{{x=-4}}}