Find x such that the distance between (x,2) and (-4,0) is 8 units. There are two solutions A and B where A < B? A= B=

1 Answer
Jim G.
May 2, 2018

#x=-4+-2sqrt15#

Explanation:

#"calculate the distance using the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(-4,0)" and "(x_2,y_2)=(x,2)#

#rArrd=sqrt((x+4)^2+4)=8#

#color(blue)"square both sides"#

#rArr(x+4)^2+4=64#

#rArr(x+4)^2=60#

#color(blue)"take the square root of both sides"#

#sqrt((x+4)^2)=+-sqrt60#

#rArrx+4=+-2sqrt15#

#rArrx=-4+-2sqrt15#

#"where "-4-2sqrt15<-4+2sqrt15#

#rArrA=-4-2sqrt15" and B "=-4+2sqrt15#

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