document.write( "Question 80094: the question says solve: 2X+6 (under a square root)- X-6(under a square root)=3
\n" ); document.write( "My teacher got X=15 but I can not figure out how he came to that conclusion, could you help me please? \n" ); document.write( "

Algebra.Com's Answer #57454 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x:
\n" ); document.write( " $\"sqrt%282x%2B6%29-sqrt%28x-6%29+=+3\"$ First, isolate the radicals if possible. Here, you can add $\"sqrt%28x-6%29\"$ to both sides.
\n" ); document.write( " $\"sqrt%282x%2B6%29+=+sqrt%28x-6%29%2B3\"$ Now square both sides to remove the radicals, well...some of them.
\n" ); document.write( " $\"2x%2B6+=+x-6%2B6sqrt%28x-6%29%2B9\"$ Simplify this. Subtract x from both sides.
\n" ); document.write( " $\"x%2B6+=+6sqrt%28x-6%29%2B3\"$ Subtract 3 from both sides.
\n" ); document.write( " $\"x%2B3=+6sqrt%28x-6%29\"$ Square both sides again to remove the remaining radical.
\n" ); document.write( " $\"x%5E2%2B6x%2B9+=+36%28x-6%29\"$ Simplify.
\n" ); document.write( " $\"x%5E2%2B6x%2B9+=+36x-216\"$ Subtract 36x from both sides.
\n" ); document.write( " $\"x%5E2-30x%2B9+=+-216\"$ Add 216 to both sides.
\n" ); document.write( " $\"x%5E2-30x%2B225+=+0\"$ Now factor this quadratic equation.
\n" ); document.write( " $\"%28x-15%29%28x-15%29+=+0\"$ Apply the zero products principle.
\n" ); document.write( " $\"x-15+=+0\"$ Add 15 to both sides.
\n" ); document.write( " $\"x+=+15\"$
\n" ); document.write( "Your teacher is correct! \n" ); document.write( "

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