we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
the center (h,k)--------> (0,0)
area of the circle=pi*r²---------> r²=A/pi----> r²=144/pi----> r²=45.86 units²
so the equation of a circle is
x²+y²=45.86
the x-intercepts of the graph is for y=0
then
x²+0²=45.86-------> x²=45.86------> x=(+/-)√45.86-----> x=(+/-)6.77
using a graph tool
see the attached figure
the solution are the points
(-6.8,0)
(6.8,0)
the answer is
the x-intercepts of the graph are the points (-6.8,0) and (6.8,0)