SOLUTION: solve: x=sqrt3x+13-5= show work please

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Question 35547: solve: x=sqrt3x+13-5=
show work please
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
+x=sqrt%283x%2B13%29-5

Start by adding +5 to each side:
+x%2B5+=sqrt%283x%2B13%29+

Next, square both sides:
+%28x%2B5%29%5E2+=+%28sqrt%283x%2B13%29%29%5E2
+x%5E2%2B10x+%2B+25+=+3x%2B13+

This is quadratic, so set it equal to zero and factor! By the way, it ALWAYS factors in radical equations like this!
x%5E2+%2B+7x+%2B+12+=+0
%28x%2B3%29%28x%2B4%29+=+0
x=-3 or x=+-4

However, these answers are NOT guaranteed! They must be checked in the original equation:

Check x = -3
+x=sqrt%283x%2B13%29-5
+-3+=+sqrt%283%2A%28-3%29%2B13%29+-+5
+-3+=+sqrt%284%29+-+5
-3+=+2-5
It checks!!

Check x = -4
+x=sqrt%283x%2B13%29-5
+-4+=+sqrt%283%2A%28-4%29%2B13%29+-+5
+-4+=+sqrt%281%29+-+5
-4+=+1-5
It also checks!!

Final answer is x= -3 or x= -4.

R^2 at SCC