Find the constant term that should be added to make the following expression a perfect-square trinomial.?

Question

x^2 + 7x

Answer 1

The constant term that should be added to is x^2 + 7x
to make it a perfect term is (7x7)/4 or 49/4.
The expression then becomes x^2 + 7x + 49/4
which is
x^2 + 2(7/2) x + (7/2)(7/2) = x^2 + 2(7/2) x + (7/2)^2
= (x +7/2) ^2
The middle term of a perfect square trinomial is found out by 2 (sq root 1st term) (sq root last term) for example in a^2 + 2ab + b^2 which is a perfect square the middle term is 2 sq root (a^2) (sq root b^2)
Using this method the last term or constant term is also found by
square (middle term) / 4 X first term
In our case middle term is 7x and 1st term is x^2 which gives a constant last term (7x)^2 /4 x^2 after x^2 gets canceled in numerator and denominator

Answer 2

Remember (x+a)² = x² + 2ax + a², so you have a=7/2 and your last term should be (7/2)² = 49/4.

Answer 3

49/4

Answer 4

2x