Question

X2 +1/2x+____=2+____?

Answer 1

`x^(2)+(1)/(2) x + (33)/(16)= 2 + (x + (1)/(4))^2`

Explanation:

`x^(2)+(1)/(2) x=x^(2)+2 * (1)/(4) * x +((1)/(4))^2 - ((1)/(4))^2`

`=[x^(2)+2 * (1)/(4) * x +((1)/(4))^2] - ((1)/(16))`

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

____________________

then

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

then

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

then

`x^(2)+(1)/(2) x = [(x + (1)/(4))^2 - ((33)/(16)) ] + 2`

then

`x^(2)+(1)/(2) x = (x + (1)/(4))^2 - (33)/(16) + 2`

then

`x^(2)+(1)/(2) x + (33)/(16)= (x + (1)/(4))^2 + 2`

then

`x^(2)+(1)/(2) x + (33)/(16)= 2 + (x + (1)/(4))^2`