Question

x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9

Answer 1

The missing number is the square-root of the constant term on the left-hand-side, which equals sqrt(1/16)=1/sqrt(16)=1/4.
Check:
(x+1/4)^2=x^2+2*(1/4)x+(1/4)^2=x^2+x/2+1/16. ok

Answer: x= 1/4

Answer 2

`(1)/(4)`

Explanation:

we have

`x^(2) +(1)/(2)x+(1)/(16)=(4)/(9)`

we know that

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

in this problem

`2ax=(1)/(2)x` ------>
`a=(1)/(4)`

`a^(2)=(1)/(16)` ----->
`a=(1)/(4)`

so

`x^(2) +(1)/(2)x+(1)/(16)=(x+(1)/(4))^(2)`

the missing number in the left side is
`(1)/(4)`