Question

What value would you add to this expression to make a perfect square? x²+x

Answer 1

we would add
`\:\left((1)/(2)\right)^2\:` or 1/4 to make the expression a perfect square.

Explanation:

Given the expression

`x^2+x`

`\mathrm{Write}\:x^2+x\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2`

`2a=1`

Divide both sides by 2

`(2a)/(2)=(1)/(2)`

`a=(1)/(2)`

as

`x^2+2ax+a^2=\left(x+a\right)^2`

`\mathrm{Add\:}\:\left((1)/(2)\right)^2\:`

`x^2+1x+\left((1)/(2)\right)^2=\left(x+(1)/(2)\right)^2`

Thus, we would add
`\:\left((1)/(2)\right)^2\:` or 1/4 to make the expression a perfect square.