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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285-x%29=x-3 Start with the given equation.


5-x=%28x-3%29%5E2 Square both sides.


5-x=x%5E2-6x%2B9 Foil the right side.


5-x-x%5E2%2B6x-9=0 Get all terms to the left side.


-x%5E2%2B5x-4=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=5, and c=-4


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%28-1%29%28-4%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=5, and c=-4


x+=+%28-5+%2B-+sqrt%28+25-4%28-1%29%28-4%29+%29%29%2F%282%28-1%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25-16+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-4%29 to get 16


x+=+%28-5+%2B-+sqrt%28+9+%29%29%2F%282%28-1%29%29 Subtract 16 from 25 to get 9


x+=+%28-5+%2B-+sqrt%28+9+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-5+%2B-+3%29%2F%28-2%29 Take the square root of 9 to get 3.


x+=+%28-5+%2B+3%29%2F%28-2%29 or x+=+%28-5+-+3%29%2F%28-2%29 Break up the expression.


x+=+%28-2%29%2F%28-2%29 or x+=++%28-8%29%2F%28-2%29 Combine like terms.


x+=+1 or x+=+4 Simplify.


So the possible answers are x+=+1 or x+=+4



However, we need to check the possible answers.


Check:

Let's check the first answer x+=+1

sqrt%285-x%29=x-3 Start with the original equation.


sqrt%285-1%29=1-3 Plug in x+=+1


sqrt%284%29=-2 Subtract.


2=-2 Take the square root of 4 to get 2.


Since this equation is not true, this means that x+=+1 is not a real solution.


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



Let's check the second answer x+=+4

sqrt%285-x%29=x-3 Start with the original equation.


sqrt%285-4%29=4-3 Plug in x+=+4


sqrt%281%29=1 Subtract.


1=1 Take the square root of 1 to get 1.


Since this equation is true, this means that x+=+4 is a real solution.




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

Answer:


So the only solution is x+=+4