Question

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

Answer 1

Isolate the square root.

Explanation:

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

Square both sides of the equation to get rid of the square root.

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

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

`x^2 + 2x + 1 = 0`

`(x + 1)(x + 1) = 0`

`x = -1`

Checking your solution in the original equation, we find our solution works. This is vital with radical equations, since extraneous solutions can arise during the solving process.

Hopefully this helps!