document.write( "Question 419382: what is 5p^2=-8+22p \n" ); document.write( "

Algebra.Com's Answer #293306 by duckness73(47) $\"\"$ $\"About$

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Starting with the original equation:
\n" ); document.write( " $\"5p%5E2=-8%2B22p\"$ \r
\n" ); document.write( "\n" ); document.write( "Let's get all of the terms on one side of the equation:
\n" ); document.write( " $\"5p%5E2+-+22p+%2B+8+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "Then factoring we have:
\n" ); document.write( "(5p - 2)(p - 4) = 0\r
\n" ); document.write( "\n" ); document.write( "Solving each factor individually, we have:
\n" ); document.write( "5p - 2 = 0 gives p = 2/5
\n" ); document.write( "p - 4 = 0 gives p = 4\r
\n" ); document.write( "\n" ); document.write( "Solution: p = 2/5 or p = 4\r
\n" ); document.write( "\n" ); document.write( "Let's check the answers:
\n" ); document.write( "For p = 2/5 we have:
\n" ); document.write( " $\"5+%28%282%2F5%29%5E2%29+=+-8+%2B+22%282%2F5%29\"$
\n" ); document.write( "5 (4/25) = -8 + (44/5)
\n" ); document.write( "20/25 = -40/5 + 44/5 (need a common denominator in order to add the fraction)
\n" ); document.write( "20/25 = 4/5
\n" ); document.write( "4/5 = 4/5 (reducing the fraction on the left side of the equation)
\n" ); document.write( "So, p = 2/5 checks out\r
\n" ); document.write( "\n" ); document.write( "For p = 4 we have:
\n" ); document.write( " $\"5+%28%284%5E2%29%29+=+-8+%2B+%2822+%284%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "5 * 16 = -8 + 88
\n" ); document.write( "80 = 80
\n" ); document.write( "So, p = 4 checks out \n" ); document.write( "

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