To determine the value of n that makes the expression x² + 11x + n a perfect square trinomial, we can use the formula for a perfect square trinomial.
A perfect square trinomial can be expressed in the general form of:
- (a + b)² = a² + 2ab + b²
Here, a is the coefficient of the x term and b is a constant. In our case, the coefficient of x is 11, relating to our perfect square trinomial.
The value of b can be derived by the equation:
- 2b = 11
Now, solving for b, we have:
- b = 11/2 = 5.5
Next, to find the value of n, we need to calculate b²:
- n = b²
Substituting the value of b:
- n = (5.5)² = 30.25
Thus, the value of n that makes the expression x² + 11x + n a perfect square trinomial is 30.25. This means the expression can be rewritten as:
- (x + 5.5)²
In conclusion, encapsulating the necessary steps, we find that:
- The value of n is 30.25