Wrong Answer for Correct Procedure? Here is a problem: Solve: (x^2  4) = x^2  10x + 16 Procedure 1: factor both sides for (x+2)(x2) = (x8 )(x2) divide out common factors (x+2) = (x 8 ) simplify 0 = 10 which is obviously wrong. Procedure 2: subtract all values on left from both sides for 0= x^2  10x + 16  x^2 + 4 simplify 0= 10x + 20 which means 10x=20 x=2 I don't understand why is the first procedure wrong while the second procedure is correct? 
In the first method, dividing by x2 isn't possible if x = 2 (because division by zero isn't defined). Hence, you should consider whether x = 2 is a solution. 
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It's almost done. Can you finish? Dan 
Hi! Thank you for your help! I think I understand your point. Because we cannot divide by zero, we know that dividing by some factor (xn) is only valid if x does not equal n, (and, conversely, that dividing by some factor (x+n) is only valid if x does not equal n). Therefore, we know that dividing by some factor (xn) is valid for all x values except for x=n. Therefore, if we find that dividing by factor (xn) renders an invalid result, or a contradiction, then x must be the only number which we understood to be that which would make the division of (xn) to be invalid namely, n. So, in a sense, dividing by 0 in the form of dividing by a factor (xn) can give you the correct answer (in a negative way) since it reveals the only number that could have led to such a contradictory result. 
In general, you have to be careful anytime you divide both sides of an equation by something involving the "unknown", x, say. Once you have arrived at one or more values for x, check to be sure that value of x does not make the divisor 0. 
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