document.write( "Question 347066: (x-5)squared-4(x-5)-21=0 \n" ); document.write( "
Algebra.Com's Answer #248169 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"%28x-5%29%5E2-4%28x-5%29-21=0\"
\n" ); document.write( "There's a clever way and a long way to solve this equation. I'll do both.

\n" ); document.write( "Clever way, using a temporary variable. This involves noticing that this equation is quadratic in (x-5). It might help you to see this if I use a temporary variable. Let q = x-5. Substituting q for x-5, your equation becomes:
\n" ); document.write( "\"q%5E2+-4q+-21+=+0\"
\n" ); document.write( "This equation is easily solved for q. Just factor it:
\n" ); document.write( "\"%28q-7%29%28q%2B3%29+=+0\"
\n" ); document.write( "Use the Zero Product property:
\n" ); document.write( "q-7 = 0 or q+3 = 0
\n" ); document.write( "Solving these we get:
\n" ); document.write( "q = 7 or q = -3
\n" ); document.write( "And last we replace q with x-5:
\n" ); document.write( "x-5 = 7 or x-5 = -3
\n" ); document.write( "Solving these we get:
\n" ); document.write( "x = 12 or x = 2

\n" ); document.write( "Clever way without a temporary variable. Eventually you will be able to solve this kind of problem without a temporary variable:
\n" ); document.write( "\"%28x-5%29%5E2-4%28x-5%29-21=0\"
\n" ); document.write( "\"%28%28x-5%29-7%29%28%28x-5%29%2B3%29+=+0\"
\n" ); document.write( "\"%28x-12%29%28x-2%29+=+0\"
\n" ); document.write( "x-12 = 0 or x-2 = 0
\n" ); document.write( "x = 12 or x = 2
\n" ); document.write( "Without the temporary variable this is a very short solution.

\n" ); document.write( "The long way to do this problem is to start by simplifying the equation. We'll square (x-5) first:
\n" ); document.write( "\"%28x-5%29%5E2-4%28x-5%29-21=0\"
\n" ); document.write( "\"x%5E2+-10x+%2B25-4%28x-5%29-21=0\"
\n" ); document.write( "Multiply next:
\n" ); document.write( "\"x%5E2+-10x+%2B25-4x+%2B20-21=0\"
\n" ); document.write( "Combine like terms:
\n" ); document.write( "\"x%5E2+-14x+%2B24=0\"
\n" ); document.write( "Factor:
\n" ); document.write( "\"%28x-12%29%28x-2%29+=+0\"
\n" ); document.write( "Zero Product property:
\n" ); document.write( "x-12 = 0 or x-2 = 0
\n" ); document.write( "Solve:
\n" ); document.write( "x = 12 or x = 2 \n" ); document.write( "
\n" );