To transform the expression x² + 3x into a perfect square trinomial, we follow the steps outlined below:
- A perfect square trinomial takes the general form of (a + b)², which expands to a² + 2ab + b².
- In our expression, we have a = x (since it corresponds to x²), and we need to determine the value of b to complete the square.
- The coefficient of x in our expression is 3. According to the perfect square trinomial formula, 2ab = 3x implies that 2x * b = 3.
- Solving for b, we rearrange to find b = rac{3}{2}.
- Now we must add b² to complete the square. Calculating b² gives us:
b² = igg( rac{3}{2}igg)² = rac{9}{4}.
Thus, to turn x² + 3x into a perfect square trinomial, we need to add </strong> </strong> </strong> </strong> </strong> </strong> 9/4.
As a result, the complete expression becomes:
x² + 3x + rac{9}{4} = igg(x + rac{3}{2}igg)².
This confirms that the constant to be added is rac{9}{4}.