Can someone help me with this?! I don’t understand :/

The solution to the equation is the point where both graphs intersect, which we can kinda eyeball to be between x=1 and x = 0. However the graphs are such that we are not able to eyeball an EXACT value, so we have to iterate to try to get a value for x as close to the actual point of intersection.

Before we start, we need to note a very important characteristic of the 2 graphs. For values of x that is less than (i.e to the left) the point of intersection, the blue graph is higher than the red graph. The reverse is true for values of x that are larger than (i.e to the right) of the intersection.

With this knowledge we can build a table with values of x that we will try and also columns to represent the blue and red graphs (see attached and follow along).

Iteration 1:

To start our iteration, we can kinda see that the intersection point is about halfway between x=1 and x=0, so lets use the midpoint of these (i.e x=0.5) as our first try. (see attached table).

We notice that at x=0.5, the value of the red graph is larger than the value of the blue graph. If we go back to your original graphs, we realize that this behavior only happens to the right of the intersection point. This means that our first guess of x=0.5 is too large. We need to pick a value that is smaller.

Iteration 2:

Knowing that our first pick is too large and the intersection point is now between x=0 and x=0.5, lets split this difference again and use the midpoint of x= 0.25 as our second iteration. From the attached table, we can see that now we end up with the the value of the red graph that is smaller than the blue graph. Once again by comparing it to the given graphs, we can conclude that x=0.25 is to the left of the intersection point.

This means the solution must be greater than x=0.25

The only choice in your possible answers which works is B. x ≈ 1/4