Question

`√(2x) + 12 = x + 8`

Answer 1

First note that
`x\ge0`; otherwise
`√(2x)` is undefined as long as we're only looking for real solutions.

We can write


`√(2x)+12=x+8`

`√(2x)=x-4`

`2x=(x-4)^2`

`2x=x^2-8x+16`

`x^2-10x+16=0`

`(x-8)(x-2)=0`


`\implies x=8,x=2`