To transform the binomial [tex]\(x^2 + 5x\)[/tex] into a perfect square trinomial, we need to find a constant term that would complete the square.
1. Take the coefficient of [tex]\(x\)[/tex] in the binomial, which is 5.
2. Divide this coefficient by 2 to find the value of [tex]\(b/2\)[/tex].
[tex]\[ \frac{5}{2} = 2.5 \][/tex]
3. Square the result to find the constant term that should be added.
[tex]\[ \left(\frac{5}{2}\right)^2 = (2.5)^2 = 6.25 \][/tex]
Hence, to transform the binomial [tex]\(x^2 + 5x\)[/tex] into a perfect square trinomial, the constant term that needs to be added is [tex]\(6.25\)[/tex].
Among the given options, none of them match directly. This could imply a mistake. The closest that matches our calculation is [tex]\(\frac{25}{4}\)[/tex], since:
[tex]\[ \frac{25}{4} = 6.25 \][/tex]
Therefore, the correct choice is [tex]\(\frac{25}{4}\)[/tex].
