This problem shows one of several different methods of factoring a quadratic expression. 48 is the constant term, and -18 is the coefficient of the x term: x^2 - 18x + 48.
Possible factors of 48 are 2*24, 3*16, 4*12, 6*8, and so on.
Next, look for factor pairs (such as -3 and -16) that sum to -18. Unfortunately, none of the listed factor pairs (above) do.
Let's experiment by using completing the square to solve this quadratic x^2 - 18x + 48 for x:
Take half of the coefficient of x, square the result, and then add, and then subtract, this result from x^2 - 18x:
x^2 - 18x + 9^2 - 9^2 = - 48
Then:
(x - 9)^2 = 81 - 48 = 33
Solving for x: x - 9 = plus or minus √33, or:
x = -(9 + √33) and x = -(9 - √33)
These roots do satisfy the figure given:
-(9 + √33) and (9 - √33), when multiplied together, produce 81 - 33 = 48.
-9 + √33 and 9 - √33, when added together, produce -18
