# 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 x^{2} + x to make it a perfect-square trinomial?

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

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

Let us complete the square for the expression x^{2} + x

## Explanation:

x^{2} + x can be re-written as x^{2} + 2(x)(1/2)

a = x and the term b is 1/2 when we compare with (a + b)^{2} = a^{2} + 2ab + b^{2}

x^{2} + x = x^{2} + 2(x)(1/2)

= x^{2} + 2(x)(1/2) + (1/2)^{2} - (1/2)^{2}

= [ x^{2} + 2(x)(1/2) + (1/2)^{2} ] - 1/4

= [ x + 1/2 ]^{2} - 1/4

x^{2} + 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 x^{2} + x.

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