on the x axis means that the y value is 0 or the point is (x,0)
distance formula
D=\(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
we know that distance is 5
the first point is (x1,y1)
the (x2,y2) is (x,0)
so
D=5
x1=-8
y1=3
x2=x
y2=0
5=\(\sqrt{(-8-x)^2+(3-0)^2}\)
5=\(\sqrt{(-8-x)^2+(3)^2}\)
5=\(\sqrt{64+16x+x^2+9}\)
5=\(\sqrt{x^2+16x+73}\)
square both sides
25=\({x^2+16x+73}\)
minus 25 both sides
0=x^2+16x+48
factor
0=(x+4)(x+12)
set each to zero
x+4=0
x=-4
x+12=0
x=-12
the points are
(-4,0) and (-12,0)
