document.write( "Question 634538: Please, make this expression a perfect square trinomial. then factor the resulting PST. \"+x%5E2-7x+\" \n" ); document.write( "
Algebra.Com's Answer #399855 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
The perfect square trinomials have the forms:
\n" ); document.write( "\"a%5E2%2B2ab%2Bb%5E2\" or
\n" ); document.write( "\"a%5E2-2ab%2Bb%5E2\"
\n" ); document.write( "To turn your expressions into a PST we must make it fit one of these patterns.

\n" ); document.write( "With a coefficient of one on the x-squared term this is rather easy:
  1. Calculate one half of the coefficient of the x-term.
  2. Calculate the square of the half you found in step 1.
  3. Normally you are doing this with an equation. And with an equation the next step is to add the square you found in step 2 to both sides of the equation. Without an equation we must find another way to add this square. What we do is add a creative version of zero. (After all, adding zero doesn't change something, does it?). You'll see what I mean by \"a creative version of zero\" shortly.
  4. The x-squared term, the x-term and the square you added are now a PST. Rewrite it in the form:
    \n" ); document.write( "\"%28x%2Bq%29%5E2\"
    \n" ); document.write( "where the \"q\" is the half number you found back at step 1.
Let's see this in action:

\n" ); document.write( "1. Calculate the half:
\n" ); document.write( "Half of 7 is 7/2

\n" ); document.write( "2. Calculate the square of the half:
\n" ); document.write( "\"%287%2F2%29%5E2+=+49%2F4\"

\n" ); document.write( "3. Add the square:
\n" ); document.write( "Since \"x%5E2%2B7x\" is not an equation, we will need to use a \"creative form of zero\":
\n" ); document.write( "\"x%5E2%2B3x%2B49%2F4%2B%28-49%2F4%29\"
\n" ); document.write( "Do you see the zero I added? 49/4+(-49/4)

\n" ); document.write( "4. Rewrite the PST
\n" ); document.write( "We just rewrite the first three terms, which is the PST. The (-49/4) just stays separate. Using the \"half\" of 7/2 to rewrite the PST we get:
\n" ); document.write( "\"%28x%2B7%2F2%29%5E2%2B%28-49%2F4%29\" \n" ); document.write( "
\n" );