document.write( "Question 289118: Under square root(3-x) + under square root(x+5)=4 \n" ); document.write( "
Algebra.Com's Answer #209498 by CharlesG2(834)\"\" \"About 
You can put this solution on YOUR website!
Under square root(3-x) + under square root(x+5)=4\r
\n" ); document.write( "\n" ); document.write( "I think you mean the following:
\n" ); document.write( "\"+sqrt%283-x%29+%2B+sqrt%28x%2B5%29+=+4+\"
\n" ); document.write( "set a = 3 - x
\n" ); document.write( "set b = x + 5
\n" ); document.write( "\"+sqrt%28a%29+%2B+sqrt%28b%29+=+4+\" (square both sides)
\n" ); document.write( "\"+a+%2B+2sqrt%28a%29sqrt%28b%29+%2B+b+=+16+\"
\n" ); document.write( "\"+a+%2B+2sqrt%28ab%29+%2B+b+=+16+\"
\n" ); document.write( "\"+2sqrt%28ab%29+=+16+-+a+-+b+\" (square both sides)
\n" ); document.write( "\"+4ab+=+%2816+-+a+-+b%29%5E2+\" (evaluate (16 - a - b)^2)
\n" ); document.write( "\"+%2816+-+a+-+b%29%2816+-+a+-+b%29+\"
\n" ); document.write( "\"+256+-+16a+-+16b+-+16a+%2B+a%5E2+%2B+ab+-+16b+%2B+ab+%2B+b%5E2+\"
\n" ); document.write( "\"+a%5E2+%2B+b%5E2+%2B+2ab+-+32a+-+32b+%2B+256+\" (returning)
\n" ); document.write( "\"+4ab+=+%2816+-+a+-+b%29%5E2+\"
\n" ); document.write( "\"+4ab+=+a%5E2+%2B+b%5E2+%2B+2ab+-+32a+-+32b+%2B+256+\"
\n" ); document.write( "\"+0+=+a%5E2+%2B+b%5E2+-+2ab+-+32a+-+32b+%2B+256+\"
\n" ); document.write( "\"+a%5E2+=+%283+-+x%29%5E2+\"
\n" ); document.write( "\"+a%5E2+=+9+-+6x+%2B+x%5E2+\"
\n" ); document.write( "\"+a%5E2+=+x%5E2+-+6x+%2B+9+\"
\n" ); document.write( "\"+b%5E2+=+%28x+%2B+5%29%5E2+\"
\n" ); document.write( "\"+b%5E2+=+x%5E2+%2B+10x+%2B+25+\"
\n" ); document.write( "\"+ab+=+%283+-+x%29%28x+%2B+5%29+\"
\n" ); document.write( "\"+ab+=+3x+%2B+15+-+x%5E2+-+5x+\"
\n" ); document.write( "\"+ab+=+-x%5E2+-+2x+%2B+15+\"
\n" ); document.write( "
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\n" ); document.write( "\"+0+=+2x%5E2+%2B+4x+%2B+34+%2B+%282x%5E2+%2B+4x+-+30%29+-+256+%2B+256+\"
\n" ); document.write( "\"+0+=+4x%5E2+%2B+8x+%2B+4+\"
\n" ); document.write( "\"+0+=+x%5E2+%2B+2x+%2B+1\"
\n" ); document.write( "\"+0+=+%28x+%2B+1%29%28x+%2B+1%29+\"
\n" ); document.write( "x = -1
\n" ); document.write( "check: \"+sqrt%283-x%29+%2B+sqrt%28x%2B5%29+=+4+\"
\n" ); document.write( "\"+sqrt%283+-+-1%29+%2B+sqrt%28-1+%2B5%29+\"
\n" ); document.write( "\"+sqrt%284%29+%2B+sqrt%284%29+\"
\n" ); document.write( "\"+2+%2B+2+=+4+\"\r
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