Consider $$ x^{2}+10 x+ $$ How many unit tiles need to be added to complete the square and form a perfect square trinomial expression? unit tiles

Question

UpStudy AI · Accepted Answer

To complete the square for the quadratic expression $$ x^{2} + 10x $$ and form a perfect square trinomial, follow these steps:

1. **Identify the Coefficient of $$ x $$:**
   The coefficient of $$ x $$ is **10**.

2. **Take Half of This Coefficient:**
   $$
   \frac{10}{2} = 5
   $$

3. **Square the Result:**
   $$
   5^2 = 25
   $$

4. **Add This Square to Complete the Square:**
   $$
   x^{2} + 10x + 25 = (x + 5)^2
   $$

So, **25 unit tiles** need to be added to $$ x^{2} + 10x $$ to complete the square and form the perfect square trinomial $$ (x + 5)^2 $$.

**Final Answer:**  
25 unit tiles must be added to complete the square.
25 unit tiles need to be added to complete the square.

Consider \( x^{2}+10 x+ \) How many unit tiles need to be added to complete the square and form a perfect square trinomial expression? unit tiles