Question

How do you solve `sqrt(3x+10) = x+2`?

Answer 1

`x = -3 or +2`

Explanation:

`sqrt(3x+10) = x+2`

Square both sides:
`3x+10 = (x+2)^2`

`3x+10 = x^2 + 4x +4`

`x^2+x-6=0`

`(x+3)(x-2) = 0`

Therefore:

Either `(x+3)= 0 -> x=-3`
Or `(x-2) = 0 -> x=+2`

Answer 2

`x=2 or x=-3`

Explanation:

`sqrt(3x+10)=x+2` ; squaring both sides `3x+10=(x+2)^2 or x^2+4x+4-3x-10=0 orx^2+x-6=0 or x^2+3x-2x-6=0 or x(x+3)-2(x+3)=0 or(x+3)(x-2)=0 :. x+3=0 or x=-3; x-2=0 or x=2`[Ans]