document.write( "Question 387696: 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\r
\n" ); document.write( "\n" ); document.write( "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. \r
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Algebra.Com's Answer #275541 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
The solutions must work simultaneously,
\n" ); document.write( " $\"%28x-1%29%28x-2%29=30\"$
\n" ); document.write( "If $\"x=31\"$ , then
\n" ); document.write( " $\"%2831-1%29%2831-2%29=30\"$
\n" ); document.write( " $\"30%2829%29=30\"$
\n" ); document.write( " $\"29=1\"$
\n" ); document.write( "So $\"x=31\"$ is not a solution.
\n" ); document.write( "Multiply out the left hand side using the FOIL method,
\n" ); document.write( " $\"x%5E2-2x-x%2B2=30\"$
\n" ); document.write( " $\"x%5E2-3x-28=0\"$
\n" ); document.write( " $\"%28x-7%29%28x%2B4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x-7=0\"$
\n" ); document.write( " $\"highlight%28x=7%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"x%2B4=0\"$
\n" ); document.write( " $\"highlight%28x=-4%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"%28x-1%29%28x-2%29=30\"$
\n" ); document.write( " $\"%287-1%29%287-2%29=30\"$
\n" ); document.write( " $\"%286%29%285%29=30\"$
\n" ); document.write( " $\"30=30\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"%28x-1%29%28x-2%29=30\"$
\n" ); document.write( " $\"%28-4-1%29%28-4-2%29=30\"$
\n" ); document.write( " $\"%28-5%29%28-6%29=30\"$
\n" ); document.write( " $\"30=30\"$
\n" ); document.write( "Solutions verified.
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