Which value must be added to the expression x^2+x to make it a perfect-square trinomial? a.1/4 b.1/2 c.1 d.4

Hello from MrBillDoesMath!

Choice A, 1/4

Discussion:

Consider the perfect square

        (x + a)^2 =   x^2 + (2a)x + a^2

The constant term (a^2) equals  1/2 the coefficient of x (i.e.  2a), squared.

Let's apply this idea to x^2 + x

x^2 + x =                                                    => as 2 * 1/2 = 1

x^2 + ( 2 * 1/2)x =

( x^2 + (2* 1/2)x +  ( 1/2) ^2 )  - (1/2) ^2  =    

    as constant term to add is 1/2 coefficient of x (that is, 1/2)  and

     (1/2)^2 - (1/2)^2 = 0

(x + 1/2) ^ 2  - (1/2)^2

In other words add the constant (1/2)^2 = 1/4, which is Choice A.

Thank you,

MrB

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