Question

Which of the following is the result of the equation below after completing the square and factoring?

Answer 1

D)
`(x + (5)/(2))^(2) = (9)/(4)`

Explanation:

Step(i):-

Given equation

x² + 5 x + 8 = 4

⇒
`x^(2) + 2 X (5)/(2) x + ((5)/(2) )^(2) - ((5)/(2) )^(2)+ 8 = 4`

Step(ii):-

By using (a + b)² = a² + 2 a b + b²

⇒
`(x + (5)/(2))^(2) - ((5)/(2) )^(2)+ 8 = 4`

⇒
`(x + (5)/(2))^(2) = 4 + ((5)/(2) )^(2) -8`

⇒
`(x + (5)/(2))^(2) = ((25)/(4) ) -4`

⇒
`(x + (5)/(2))^(2) = ((25-16)/(4) )`

⇒
`(x + (5)/(2))^(2) = (9)/(4)`

Final answer:-

`(x + (5)/(2))^(2) = (9)/(4)`