document.write( "Question 442268: Completing the square p squared+16p-22 \n" ); document.write( "

Algebra.Com's Answer #305020 by ilana(307) $\"\"$ $\"About$

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If you add and subtract the same number, the expression's value doesn't change. That's why completing the square works.
\n" ); document.write( "So we want to make p^2 + 16p + _ a perfect square trinomial. That means p^2 + 16p + _ can be written (p + _)^2.
\n" ); document.write( "In general, (a + b)^2 = a^2 + 2ab + b^2.
\n" ); document.write( "In this case, a=p, so 2b=16. Therefore, b=8.
\n" ); document.write( "So b^2, the last term in the perfect square trinomial, is 64.
\n" ); document.write( "So the completed square expression is:
\n" ); document.write( "(p^2 + 16p + 64) - 22 - 64, or (p + 8)^2 - 86 \n" ); document.write( "

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