document.write( "Question 922468: Please help me solve this radical equation:\r
\n" ); document.write( "\n" ); document.write( "√x+9 + √x-7 = 8 ? \n" ); document.write( "

Algebra.Com's Answer #559647 by KMST(5328) $\"\"$ $\"About$

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$\"sqrt%28x%2B9%29%2Bsqrt%28x-7%29=8\"$
\n" ); document.write( "Separating the square roots, we get
\n" ); document.write( " $\"sqrt%28x%2B9%29=8-sqrt%28x-7%29\"$
\n" ); document.write( "We square both sides to get less square roots.
\n" ); document.write( "Thwn we can square again to have no square roots.
\n" ); document.write( "We will find all the solutions (plus maybe some extraneous solutions),
\n" ); document.write( "and we will check at the end.
\n" ); document.write( " $\"%28sqrt%28x%2B9%29%29%5E2=%288-sqrt%28x-7%29%29%5E2\"$
\n" ); document.write( " $\"x%2B9=64-16sqrt%28x-7%29%2Bx-7\"$
\n" ); document.write( " $\"9=64-16sqrt%28x-7%29-7\"$
\n" ); document.write( " $\"16sqrt%28x-7%29=64-7-9\"$
\n" ); document.write( " $\"16sqrt%28x-7%29=48\"$
\n" ); document.write( "dividing both sides by 16, we get
\n" ); document.write( " $\"sqrt%28x-7%29=3\"$
\n" ); document.write( "Squaring again,
\n" ); document.write( " $\"x-7=9\"$
\n" ); document.write( " $\"x=7%2B9\"$
\n" ); document.write( " $\"x=16\"$
\n" ); document.write( "
\n" ); document.write( "Checking:
\n" ); document.write( " $\"sqrt%2816%2B9%29%2Bsqrt%2816-7%29=sqrt%2825%29%2Bsqrt%289%29=5%2B3=8\"$
\n" ); document.write( "The solution found checks out.
\n" ); document.write( " $\"highlight%28x=16%29\"$ \n" ); document.write( "

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