Answer:
Given the expression x2 + 16x.
If the quadratic equation is of the form ax2 + bx + c then to complete square
Step1: Take coefficient of x2 common from ax2 + bx + c,
⇒ a[x2 + (b/a)x + (c/a)]
Step2: Add and subtract (1/2 coefficient x)2 to quadratic term then,
⇒ a [(x + 1/2 coefficient x)2) + (c/a) - (1/2 coefficient x)2
⇒ a [(x + b/2a)2 + c/a - (b/2a)2]
Note that if the coefficient of x2 is 1 then we have to add (1/2 coefficient x)2 to convert it into perfect square expression.
Thus, in the given problem x2 + 16x.
1/2 coefficient of x = (1/2) × 16 = 8
We have to add 82 = 64, to convert it into a perfect square.
Therefore, 64 must be added to the expression to make it a perfect-square trinomial.