Final answer:
To complete the square for the expression x^2 + (5/4)x + c, the value of c is found using the formula (b/2a)^2. In this case, c = (25/64), which is 1.5625. Therefore, the correct answer is option b. 1.5625.
Step-by-step explanation:
The value of c that will complete the square in the expression x2 + \(\frac{5}{4}x \) + c can be found by using the formula to complete the square, which is \(\left(\frac{b}{2a}\right)^2\), where a is the coefficient of x2 and b is the coefficient of x. Since a = 1 and b = \(\frac{5}{4}\), we can calculate c as follows:
c = \left(\frac{\frac{5}{4}}{2}\right)^2 = \left(\frac{5}{8}\right)^2 = \frac{25}{64}
Thus, the value of c that completes the square is \(\frac{25}{64} \), which is equivalent to option b. 1.5625.