SOLUTION: In solving the equation (x + 1)(x � 2) = 54, Eric stated that the solution would be x + 1 = 54 => x = 53 or (x � 2) = 54 => x = 56 However, at least one of these solutions fail

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Question 409982: In solving the equation (x + 1)(x � 2) = 54, Eric stated that the solution would be
x + 1 = 54 => x = 53
or
(x � 2) = 54 => x = 56
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
I have tried this, when I substituted 53, and 56..I got 2862=54..I am way off..Please help..Thank you.
Found 3 solutions by richard1234, ewatrrr, stanbon:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website!
I don't know why I've seen so many problems with Eric struggling with a quadratic...

And no, it doesn't work because the 0-property rule only applies with 0. We cannot set each variable to 54 because the other variable can alter the value. The best way is to expand the left side and obtain

--> . Factoring, this becomes

--> now we can use the 0-property rule, x = 8 or x = -7 are the roots.

Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!

Hi
(x + 1)(x � 2) = 54
This equation states it is the PRODUCT of (x+1) and (x-2) = 54!
Note: The factor theorem states that a polynomial f(x) has a factor (x − k)
where k is a 'solution' if and only if f(k) = 0
(x + 1)(x � 2) = 54 |Putting this in the form ax^2 + bx + c = 0 in order to factor
x^2 -x - 2 = 54
x^2 -x - 56 = 0 |Yes!
factoring
(x-8)(x+7)= 0 |NOW! 'Each' of the Products is = 0
(x-8)= 0 x = 8
(x+7)= 0 x = -7
CHECKING our Answer(s)***
(x + 1)(x � 2) = 54
9*6 = 54
-6*-9 =54

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
In solving the equation (x + 1)(x � 2) = 54, Eric stated that the solution would be
x + 1 = 54 => x = 53
or
(x � 2) = 54 => x = 56
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
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We are told that (x+1)(x-2) = 54.
If x+1=54 then x-2 would have to equal 1 so the product could be 54
--
Then x would have to be 53 and x would have to be 3 at the same time.
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But that is impossible.
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Your substitution reveals the contradiction very well.
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Cheers,
Stan H.
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