Question

X^2 + 1/2 x + __ = 2 + __

Completing the square

Answer 1

x^2 + 1/2 x + 1/16 = 2 + 1/16.

Explanation:

The missing value is (1/2 / 2 )^2 = (1/4)^2 = 1/16.

because ( x + 1/4)^2 = x^2 + 1/2 x + (1/4)^2.

Answer 2

`(x+(1)/(4) ) ^(2)=((√(33) )/(4)) ^(2)`

Explanation:

`x^(2) +(1)/(2) x+...=2+...\\\\x^(2) +2(1)/(4) x+((1)/(4))^(2) =2+((1)/(4))^(2) \\\\(x+(1)/(4) ) ^(2)=2+(1)/(16) \\\\(x+(1)/(4) ) ^(2)=(33)/(16)\\}\\(x+(1)/(4) ) ^(2)=((√(33) )/(4)) ^(2)`