Complete the expression so it forms a perfect-square trinomial.

x² - 5x +

x² -5x + (5/2)²

Step-by-step explanation:

x² -5x + b² = (x + y)² = x² + 2xy + y²

-5x = 2xy   ∴-5 = 2y       y = - 5/2

b² = y²       b = y = - 5/2

Expression: x² -5x + 25/4 = (x - 5/2)²

The perfect-square trinomial is x^2 - 5x + 25/4 = (x - 5/2)^2

Step-by-step explanation:

A perfect square trinomial is someting like:

(a + b)^2 = a^2 + b^2 + 2ab

then, if we have:

x^2 -5x +

one of the therms is a = x, let's find b.

-5 = 2b

then b = -5/2

then we have:

x^2 - 5x + (5/2)^2 = x^2 - 5x + 25/4 = (x - 5/2)^2