document.write( "Question 292167: Find a number so that the square of the number is 28 more than three times the number. Thank you \n" ); document.write( "

Algebra.Com's Answer #211121 by Earlsdon(6294) $\"\"$ $\"About$

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Let n = the required number, then:
\n" ); document.write( " $\"n%5E2+=+3n%2B28\"$ Rearrange into the standard form for a quadratic equation.
\n" ); document.write( " $\"n%5E2-3n-28+=+0\"$ Factor this quadratic equation.
\n" ); document.write( " $\"%28n%2B4%29%28n-7%29+=+0\"$ Apply the \"zero product\" rule.
\n" ); document.write( " $\"n%2B4+=+0\"$ or $\"n-7+=+0\"$ so that...
\n" ); document.write( " $\"highlight%28n+=+-4%29\"$ or $\"highlight%28n+=+7%29\"$
\n" ); document.write( "So there are two answers to this problem. Let's check them both:
\n" ); document.write( " $\"n%5E2+=+3n%2B28\"$ Substitute n = -4.
\n" ); document.write( " $\"%28-4%29%5E2+=+3%28-4%29%2B28\"$
\n" ); document.write( " $\"16+=+-12%2B28\"$
\n" ); document.write( " $\"16+=+16\"$ OK for n = -3.
\n" ); document.write( " $\"n%5E2+=+3n%2B28\"$ Substitute n = 7.
\n" ); document.write( " $\"7%5E2+=+3%287%29%2B28\"$
\n" ); document.write( " $\"49+=+21%2B28\"$
\n" ); document.write( " $\"49+=+49\"$ OK for n = 7. \n" ); document.write( "

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