What value of Q will make the expression 4x2 + 5x + Q a complete square?

What value of Q will make the expression 4x2 + 5x + Q a complete square?

Answer Details

4x2 + 5x + Q
To make a complete square, the coefficient of x2 must be 1
= x2 + $\frac{5x}{4}$ + $\frac{Q}{4}$
Then (half the coefficient of x2) should be added
i.e. x2 + $\frac{5x}{4}$ + $\frac{25}{64}$
? $\frac{Q}{4}$ = $\frac{25}{64}$
Q = $\frac{4\times 25}{64}$
= $\frac{25}{16}$