Question

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

x² - 5x +

Answer 1

x² -5x + (5/2)²

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

Answer 2

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

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