To form a perfect square trinomial from the expression x² + 6x, we need to determine the constant that completes the square.
First, let’s recall the formula for a perfect square trinomial, which is (a + b)² = a² + 2ab + b². In our case, ‘a’ corresponds to x and ‘2b’ is equivalent to the coefficient of x, which is 6. So, we have:
- a = x
- 2b = 6 ⟹ b = 3
Now, we need to compute b²:
- b² = 3² = 9
Thus, the constant we need to add to the expression x² + 6x to make it a perfect square trinomial is 9. Therefore, we can rewrite the expression as:
x² + 6x + 9 = (x + 3)²
In conclusion, the constant that can be added to x² + 6x to form a perfect square trinomial is 9.