SOLUTION: x+3=square root of x+15

Question 96890: x+3=square root of x+15
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!

Square both sides.

subtract x+15 from both sides.
(x-1)(x+6)=0
x=1 x=-6
Check:
ok

x=1 is the only correct answer.
Ed
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