Question

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 1

this is the soltuion:

\[ (x + 4)(x – 7) = -18\]
expand left hand side:
\[ (x^2-3x-28 = -18\]
bring the -18 in:
\[ x^2-3x-10=0\]
now factor again:
\[ (x-5)(x+2)=0\]

so now:

\[ (x-5)=0\]

OR

\[ (x+2)=0\]

So: x=+5 OR x= -2