document.write( "Question 570907: what natural can replace B to make perfect square trinomial\r
\n" ); document.write( "\n" ); document.write( "64X^2+BX+16 \n" ); document.write( "

Algebra.Com's Answer #367847 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+f%28x%29+=+64x%5E2+%2B+b%2Ax+%2B+16+\"$
\n" ); document.write( "The quadratic formula to find roots is:
\n" ); document.write( " $\"x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+64+\"$
\n" ); document.write( " $\"+b+=+b+\"$
\n" ); document.write( " $\"+c+=+16+\"$
\n" ); document.write( "To make $\"+f%28x%29+\"$ a perfect square, $\"+b%5E2+-+4%2Aa%2Ac+\"$
\n" ); document.write( "must be zero
\n" ); document.write( " $\"+b%5E2+-+4%2Aa%2Ac++=+0+\"$
\n" ); document.write( " $\"+b%5E2+-+4%2A64%2A16+=+0+\"$
\n" ); document.write( " $\"+b%5E2+-+4096+=+0+\"$
\n" ); document.write( " $\"+b%5E2+=+4096+\"$
\n" ); document.write( " $\"+b+=+64+\"$
\n" ); document.write( " $\"+b+=+-64+\"$
\n" ); document.write( "-----------
\n" ); document.write( "If $\"+b+=+64+\"$
\n" ); document.write( " $\"+f%28x%29+=+64x%5E2+%2B+b%2Ax+%2B+16+\"$
\n" ); document.write( " $\"+f%28x%29+=+64x%5E2+%2B+64x+%2B+16+\"$
\n" ); document.write( " $\"+f%28x%29+=+4x%5E2+%2B+4x+%2B+1+\"$
\n" ); document.write( " $\"+f%28x%29+=+%28+2x+%2B+1+%29%5E2+\"$
\n" ); document.write( "-----------
\n" ); document.write( "If $\"+b+=+-64+\"$
\n" ); document.write( " $\"+f%28x%29+=+64x%5E2+-+64x+%2B+16+\"$
\n" ); document.write( " $\"+f%28x%29+=+4x%5E2+-+4x+%2B+1+\"$
\n" ); document.write( " $\"+f%28x%29+=+%28+2x+-+1+%29%5E2+\"$
\n" ); document.write( "-----------
\n" ); document.write( " $\"b\"$ can be replaced with either $\"+64+\"$ or $\"+-64+\"$
\n" ); document.write( "Here are plots of the 2 alternatives:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+8%2C+4x%5E2+%2B+4x+%2B+1%2C+4x%5E2+-+4x+%2B+1+%29+\"$ \n" ); document.write( "

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