Question

Use the bisection method to find an approximate solution for the equation
x^2+x=1

Start with the interval [0,1].

Answer 1

What size interval do you require?

Answer 2

For an interval of size 0.5:
f(0)=-1, f(1)=1, f(0.5)=-0.25
Therefore, the root lies in the interval: \[0.5< x < 1\] (because there is a sign change).
Then repeat the process as necessary, each time using the midpoint of the previous interval to form the new interval.