Which Value Must Be Added to the Expression X2 + X to Make It a Perfect-square Trinomial?


Question: Which value must be added to the expression x2 + x to make it a perfect-square trinomial?

Completing the square is converting a quadratic expression of the form ax+ bx +c to the vertex form  a(x+d)2 + e

Answer: [ x + 1/2 ]2 - 1/4 = x2 + x  will be a perfect-square trinomial if we add 1/4 to the expression.

Let us complete the square for the expression x2 + x

Explanation:

x2 + x can be re-written as x2 + 2(x)(1/2)

a = x and the term b is 1/2 when we compare with (a + b)2 = a2 + 2ab + b2

x2 + x = x2 + 2(x)(1/2)

= x2 + 2(x)(1/2) + (1/2)2 - (1/2)2

= [ x2 + 2(x)(1/2) + (1/2)2 ] - 1/4

= [ x + 1/2 ]2 - 1/4

x2 + x will be a perfect-square trinomial if we add 1/4 to the expression.

Thus, [ x + 1/2 ]2 - 1/4 is the vertex form of the given expression x2 + x.