Question

Solve : 
`2x - 3 = sqrt(2x^2 - 2x + 21)` 

Answer 1

Given : `2x - 3 = sqrt(2x^2 - 2x + 21)` 

by squaring on both side

`(2x - 3)^2 = 2x^2 - 2x + 21`

`(2x)^2 + (3)^2 - (2) (2x) (3) = 2x^2 - 2x + 21`

`4x^2 + 9 - 12x = 2x^2 - 2x + 21`

`2x^2 = 10x + 12`

`2x^2 - 10x - 12 = 0`

by splitting the mid term

`2x^2 - 12x + 2x - 12 = 0`

`2x (x - 6) + (x - 6) = 0`

`(2x + 2) (x - 6) = 0`

here the values of x are 

2x + 2 = 0

x = -1

x - 6 = 0

x = 6