SOLUTION: x+3=sq.root x+15

Question 96897: x+3=sq.root x+15
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Does your problem look like this:

Start with the given equation

Square both sides

Foil

Get all terms to one side

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=5, and c=-6

Square 5 to get 25

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our possible solutions are:
or

Let's check them:

Let's check the solution x=-6
Start with the given equation

Plug in x=-6

Combine like terms

Take the square root of 9. Since this is not true, x=-6 is not a solution (it's extraneous)

Let's check the solution x=1

Start with the given equation

Plug in x=1

Combine like terms

Take the square root of 16. Since this is true, x=1 is a solution

So our only solution is
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