SOLUTION: square root of 5-x =x-3 How do i solve this. I've tried squaring both sides but when it comes to figuring out the two possibilities it never comes out understandable...can u pleas

Question 147372: square root of 5-x =x-3
How do i solve this. I've tried squaring both sides but when it comes to figuring out the two possibilities it never comes out understandable...can u please help and show some steps for me.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Square both sides.

Foil the right side.

Get all terms to the left side.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, we need to check the possible answers.

Check:

Let's check the first answer

Start with the original equation.

Plug in

Subtract.

Take the square root of 4 to get 2.

Since this equation is not true, this means that is not a real solution.

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

Let's check the second answer

Start with the original equation.

Plug in

Subtract.

Take the square root of 1 to get 1.

Since this equation is true, this means that is a real solution.

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

Answer:

So the only solution is
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