Question

What is the solution set of the quadratic equation 1/2 (4x-1) ^2 = 4 ​

Answer 1

x =
`(1)/(4)` ±
`(1)/(2)`
`√(2)`

Explanation:

Given

`(1)/(2)` (4x - 1)² = 4 ( multiply both sides by 2 to clear the fraction )

(4x - 1)² = 8 ( take the square root of both sides )

4x - 1 = ±
`√(8)` = ± 2
`√(2)` ( add 1 to both sides )

4x = 1 ± 2
`√(2)` ( divide both sides by 4 )

x =
`(1+/-2√(2) )/(4)`

=
`(1)/(4)` ±
`(1)/(2)`
`√(2)`