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_________
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
