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

Answer:

$\frac{1}{4}$

Step-by-step explanation:

we have

$x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}$

we know that

$(x+a)^{2}=x^{2}+2ax+a^{2}$

in this problem

$2ax=\frac{1}{2}x$ ------> $a=\frac{1}{4}$

$a^{2}=\frac{1}{16}$ -----> $a=\frac{1}{4}$

so

$x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}$

the missing number in the left side is $\frac{1}{4}$

Answer 2

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