Which value must be added to the expression x²-3x to make it a perfect-square trinomial?

Solution:

Given: Expression is x² - 3x

Standard form of a perfect square trinomial is

(x - a)² = x² - 2ax + a²

Add c as the value that must be added in the given equation

x² - 3x + c

Now let us equate it to the standard form

3x = 2ax, c =  a²

So we get,

3x = 2ax

a = 3/2

c = (3/2)² = 9/4

Here,

(x - 3/2)² = x² - 3x + 9/4

Therefore, the value that must be added is 9/4.

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Which value must be added to the expression x² - 3x to make it a perfect-square trinomial?

Summary:

The value that must be added to the expression x² - 3x to make it a perfect-square trinomial is 9/4.