Question

How do you solve `sqrt(x+12)=x`?

Answer 1

`sqrt(x+12) =x`

squaring both the sides
`(sqrt(x+12))^2 =x^2`
`x+12 = x^2`
`x^2 -x -12 =0`

we can find the roots by Splitting the Middle Term of this expression to factorise it:

`x^2 -x -12 = x^2 -4x +3x -12`
`= x(x-4)+3 (x-4)`
`= (x+3)(x-4)`

the solution is `color(blue)x=-3 , color(blue)x=4`