SOLUTION: 1. In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be x – 1 = 30 => x = 31 or (x – 2) = 30 => x = 32 However, at least one of these solutions f

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 1. In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be x – 1 = 30 => x = 31 or (x – 2) = 30 => x = 32 However, at least one of these solutions f      Log On


   

Question 509261: 1. In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be
x – 1 = 30 => x = 31
or
(x – 2) = 30 => x = 32
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.

MATH GENIUS I NEED HELP I AM LOST AND ON A DEADLINE!!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
They call it the "zero-product property" for a reason.

You should expand and simplify it first.



This can be factored to



Now we can use the zero-product property and obtain x = 7 and x = -4 as our solutions.