To determine the value that needs to be added to the expression x² + 3x to form a perfect square trinomial, we can use the method of completing the square.
A perfect square trinomial can generally be expressed in the form (a + b)² = a² + 2ab + b². In this case, we have the coefficient of x as 3, which means we can first find the value of b.
To find b, we take half of the coefficient of x (which is 3) and then square it:
- Half of 3 is 3/2.
- Squaring 3/2 gives us (3/2)² = 9/4.
Thus, we need to add 9/4 to the expression x² + 3x in order to get a perfect square trinomial:
x² + 3x + 9/4 = (x + 3/2)².
Final answer: 9/4 must be added to make the expression a perfect square trinomial.