SOLUTION: In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be x + 4 = -18 => x = -22 or (x – 7) = -18 => x = -11 However, at least one of these solutions

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be x + 4 = -18 => x = -22 or (x – 7) = -18 => x = -11 However, at least one of these solutions      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 426045: In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be
x + 4 = -18 => x = -22
or
(x – 7) = -18 => x = -11
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.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

(x + 4)(x – 7) = -18

this NOT to say:  (x+4) = -18  and (x-7) = -18



The factor theorem states that a polynomial f(x) has a factor (x − k) 

if and only if f(k) = 0

(x + 4)(x – 7) = -18

x^2 - 3x - 28 = -18

x^2 - 3x -10 = 0

FACTORING

(x -5)(x+2) = 0    |  this DOES say (x-5) and/or (x+2)  = 0

(x -5)=0  x = 5

(x +2)=0  x = -2



CHECKING our Answers***

 25-15-28 = -18    | x = 5

4 + 6 - 28 = -18   | x = -2