Question

Complete the square : x^2+3/2x+1 (can you please help me solve it?)

Answer 1

X^2+3/2x+1=0
multiplying all the terms by 2
Now the equation is:
2(X^2)+2(3/2X)+2(1) =0
2X^2+3X+2=0

Answer 2

(x +
`(3)/(4)` )² +
`(7)/(16)`

Explanation:

x² +
`(3)/(2)` x + 1

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² +
`(3)/(2)` x

= x² + 2(
`(3)/(4)` )x + (
`(3)/(4)` )² - (
`(3)/(4)` )² + 1

= (x +
`(3)/(4)` )² -
`(9)/(16)` +
`(16)/(16)`

= (x +
`(3)/(4)` )² +
`(7)/(16)`