f(0)=-2, f(3)=9-2=7. We want to find the value of x such that f(x)=0.
Since 0 lies between -2 and 7, we divide the interval in half and calculate f(1.5)=1.52-2=2.25-2=0.25.
This result is greater than zero so we now halve the interval between 0 and 1.5, because f(0)<0 and f(1.5)>0, so f(x)=0 somewhere between x=0 and 1.5. Bisect this interval and x=0.75.
f(0.75)=-1.4375. Therefore the root lies between x=0.75 and 1.5. Halfway between these is their average=1.125. f(1.125)=-0.734375. The root lies between 1.125 and 1.5, which average to 1.3125.
f(1.3125)=-0.27734375. The root lies between x=1.3125 and 1.5, which average to 1.40625. f(1.40625)=-0.0224609375. But this is less than the error of ±0.1, so x=1.4 is an approximate root of the function.