Answer:
To express the quadratic expression x^2 - 5x + 8 in the form of (x - a)^2 + b, we need to complete the square. To do this, we can add and subtract the square of half the coefficient of the x term. In this case, that would be (1/2)(-5) = -5/2. Therefore, we add and subtract (1/2)(-5)^2 = (-5/2)^2 = 25/4 to get:
x^2 - 5x + 8 = (x^2 - 5x + (25/4)) + (8 - (25/4))
Next, we need to add and subtract 25/4 in such a way that we can factor the quadratic expression as the square of a binomial. To do this, we add 25/4 to the first term and subtract 25/4 from the second term to get:
x^2 - 5x + (25/4) + (8 - (25/4)) = (x^2 - 5x + 25/4) + (8 - 25/4)
Now we can factor the quadratic expression as the square of a binomial:
(x^2 - 5x + 25/4) + (8 - 25/4) = (x - 5/2)^2 + (8 - 25/4)
Therefore, we can express x^2 - 5x + 8 in the form of (x - a)^2 + b where a is -5/2 and b is 8 - 25/4.
Note that the values of a and b are not whole numbers because we added and subtracted a fraction when completing the square.