A "root" is an x value that you plug in that leads the left side to turn into zero.
There are two possible roots. Let's factor the left side to find them
To factor, find two numbers that multiply to -32 and add to -14. These two numbers are -16 and 2
Note how
-16 plus 2 = -14
-16 times 2 = -32
So this means,
x^2-14x-32
turns into
(x-16)(x+2)
Now use the zero product property
(x-16)(x+2) = 0
x-16 = 0 or x+2 = 0
x = 16 or x = -2
The two roots are 16 and -2 which go in the two answer boxes
If we plugged in x = 16, into the original equation, we'd be left with 0 = 0. The same can be said about x = -2 as well. This is why these two values are the roots.
Note: "root" is the same as "x-intercept" if the root is a real number.