Need help on how to do this problem!!

Question

Solve for :

       

The lower (or only) solution for this equation is    

The higher solution for this equation is    

The solution     is an extraneous solution (if any).

(Fill in each with an integer or a rational number or the word "none" or "n/a" with no capital letters or quotation marks.)

Answer 1

With square root problems, it is important to first figure out what an acceptable domain can be for x.

We are only going to be considering real solutions to the problem, not imaginary or complex ones, so we will say that you can't take the square root of a negative number. That means that the expression under the square root can't be less than zero-- 2x + 15 must be greater than or equal to zero.

This means that x must be greater than or equal to -7.5 and we will keep that in mind as we work through the problem.

You will want to square both sides of the equation in order to work towards solving for x.

After you square both sides, you will have 2x + 15 = (x+6)².

Use FOIL to

expand (x+6)² to x² + 12x + 36

Now you should have

2x + 15 = x² + 12x + 36

Since this is a quadratic equation now with an x² term, you want rearrange all of your terms on one side of the equation with zero on the other side. Subtract 2x from both sides and combine like terms and then subtract 15 from both sides and combine like terms.

You should end up with this:

x² + 10x + 21 = 0

Now it is up to you to factor this or solve with the quadratic formula to find the solutions.

Before you write down any solutions you find as answers, remember that they are extraneous if they are less than -7.5!