SOLUTION: x = √ (16x + 225)

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Question 416819: x = √ (16x + 225)
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


     _________
x = √16x + 225

Square both sides
       _________
x² = (√16x + 225)²

x² = 16x + 225

x² - 16x - 225 = 0

(x - 25)(x + 9) = 0

x - 25 =  0      x + 9 =  0
     x = 25          x = -9 

We must always check a radical equation
Checking x = 25:

      _________
 x = √16x + 225
      ____________
25 = √16(25) + 225
      _________
25 = √400 + 225
      ___
25 = √625

25 = 25
 
So x = 25 is a solution.

Checking x = -9:

      _________
 x = √16x + 225
      ____________
-9 = √16(-9) + 225
      __________
-9 = √-144 + 225
      __
-9 = √81

-9 = 9
 
That is false, so x = -9 is not a solution.  (But please don't get
the idea that you discarded -9 because it is negative, as in
many cases a negative solution checks. It just didn't happen to
in this case).

Edwin
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