Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.

From the given function, the x-intercepts will be calculated as follows:
at x-intercept f(x)=0, thus when f(x)=0
f(x)=7x^2+9x+1
we shall have:
0=7x^2+9x+1
solving the above using quadratic formula the above we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
from the function, a=7, b=9 and c=1
thus plugging the values in the formula we obtain:
x=[-9+/-sqrt(9^2-4(7*1))]/(2*7)
x=[-9+/-sqrt(53)]/14
x=-9/14+√54/14
or
x=-9/14-√54/14
thus the x-intercepts are the values of x