Question

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

(x^2 - 5x + \frac{25}{4})

(x^2 + \text{ }x + 49)
options for the dropdown:
14
7
7/2

Explanation:

⚡ Using what you learned: completing the square

Step 1: Identify the structure of a perfect-square trinomial

A perfect-square trinomial has the form:

$$ (x + a)^2 = x^2 + 2ax + a^2 $$

Step 2: Find the value of \( a \)

Compare the given expression \( x^2 + \text{___}x + 49 \) to the standard form \( x^2 + 2ax + a^2 \):

$$ a^2 = 49 $$

$$ a = \sqrt{49} = 7 $$

Step 3: Calculate the middle coefficient

The coefficient of the middle term is \( 2a \):

$$ 2a = 2(7) = 14 $$

Answer:

14