document.write( "Question 145996: how to solve problem y+6square root y=16? they say the answer is 4, but i don't know how they came to that conclusion \n" ); document.write( "

Algebra.Com's Answer #106555 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y+%2B+6%2Asqrt%28y%29+=+16\"$
\n" ); document.write( "I define a new variable to be $\"z%5E2+=+y\"$
\n" ); document.write( "Taking the square root of both sides, $\"z+=0+%2B-sqrt%28y%29\"$
\n" ); document.write( "Sustituting,
\n" ); document.write( " $\"z%5E2+%2B+6z+-16+=+0\"$
\n" ); document.write( " $\"%28z+%2B+8%29%28z+-+2%29+=+0\"$
\n" ); document.write( " $\"z+=+-8\"$
\n" ); document.write( " $\"z+=+2\"$
\n" ); document.write( "Putting $\"z\"$ back in terms of $\"y\"$
\n" ); document.write( " $\"-sqrt%28y%29+=+-8\"$
\n" ); document.write( " $\"y+=+64\"$
\n" ); document.write( "and
\n" ); document.write( " $\"sqrt%28y%29+=+2\"$
\n" ); document.write( " $\"y+=+4\"$
\n" ); document.write( "Now I substitute these answers in the original equation
\n" ); document.write( " $\"y+%2B+6%2Asqrt%28y%29+=+16\"$
\n" ); document.write( " $\"64+-+6%2A8+=+16\"$
\n" ); document.write( " $\"64+-+48+=+16\"$
\n" ); document.write( " $\"16+=+16\"$
\n" ); document.write( "and
\n" ); document.write( " $\"4+%2B+6%2A2+=+16\"$
\n" ); document.write( " $\"4+%2B+12+=+16\"$
\n" ); document.write( "It looks like they are only allowing $\"sqrt%28y%29\"$ to be
\n" ); document.write( "positive, so $\"y+=+4\"$ and $\"sqrt%28y%29+=+2\"$ are the answers \n" ); document.write( "

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