Expert: Bobby Soltani - 10/11/2009

Question
Hi,
I really need help with this question because at first I though I could solve it in a snap but...I am getting very weird answers!! Here is the problem:

Sqrt(2x+7)   - x =2

Thanks ALOT,

Please reply quickly,

Saaketh

Answer
Hi Saaketh,

SQRT(2x+7) - x = 2

add x to both sides

SQRT(2x+7) = x+2

Square both sides

2x + 7 = x^2 + 4x + 4

subtract (2x+7) from both sides

0 = x^2 + 2x - 3

factor the right side

0 = (x + 3)(x - 1)

x = -3 and 1

But, we are not done.  When solving radical equations, extra solutions may come up when you raise both sides to an even power.  These extra solutions are called extraneous solutions. If a value is an extraneous solution, it is not a solution to the original problem.  In radical equations, you can check for extraneous solutions by plugging in the values you found back into the original problem. If the left side does not equal the right side, then you have an extraneous solution.

So, only x=1 is a solution since x=-3 is not a solution to the original equation.

Hope that helps,

Bobby