SOLUTION: solve the radical equation check your solutions /2y+7+4=y

Question 97129: solve the radical equation check your solutions
/2y+7+4=y
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!

y = 9 and y = 1
y = 1 doesn't work ... y = 9 is the only answer
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Your problem looks like this right?

Subtract 4 from both sides

Square both sides

Foil

Get all terms to one side

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

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-10, and c=9

Negate -10 to get 10

Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .)

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

------------------------------------------------------------------

Now we have to check our answers:

Lets check y=9

Start with the given equation

Plug in

Multiply

Add

Take the square root

Add. Since the equation is true, y=9 is a solution

----------------------

Lets check y=1

Start with the given equation

Plug in

Multiply

Add

Take the square root

Add. Since the equation is not true, y=1 is a not a solution

Answer:

So our only solution is
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