Respuesta :

mathmate
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
calculista

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we have

[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]

we know that

[tex](x+a)^{2}=x^{2}+2ax+a^{2}[/tex]

in this problem

[tex]2ax=\frac{1}{2}x[/tex] ------> [tex]a=\frac{1}{4}[/tex]

[tex]a^{2}=\frac{1}{16}[/tex] -----> [tex]a=\frac{1}{4}[/tex]

so

[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}[/tex]

the missing number in the left side is [tex]\frac{1}{4}[/tex]


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