document.write( "Question 162354: sqrt(x+2) + sqrt(3x+4) = 2 \n" ); document.write( "

Algebra.Com's Answer #119687 by gonzo(654) $\"\"$ $\"About$

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$\"sqrt%28x%2B2%29+%2B+sqrt%283%2Ax%2B4%29+=+2\"$
\n" ); document.write( " $\"sqrt%28x%2B2%29+=+2+-+sqrt%283%2Ax%2B4%29\"$
\n" ); document.write( "multiply both sides by $\"sqrt%28x%2B2%29\"$ to get
\n" ); document.write( " $\"x%2B2+=+sqrt%28x%2B2%29%2A%282-sqrt%283%2Ax%2B4%29%29\"$
\n" ); document.write( "since $\"sqrt%28x%2B2%29+=+2+-+sqrt%283%2Ax%2B4%29\"$
\n" ); document.write( "this equation becomes
\n" ); document.write( " $\"x%2B2+=+%282+-+sqrt%283%2Ax%2B4%29%29%2A%282-sqrt%283%2Ax%2B4%29%29\"$
\n" ); document.write( "which is the same as
\n" ); document.write( " $\"x%2B2+=+%282-sqrt%283%2Ax%2B4%29%29%5E2\"$
\n" ); document.write( "multiplying out on the right hand side of the equation and it becomes
\n" ); document.write( " $\"x%2B2+=+4+-+4%2Asqrt%283%2Ax%2B4%29+%2B+%283%2Ax+%2B+4%29\"$
\n" ); document.write( "this becomes
\n" ); document.write( " $\"x%2B2+=+4+-+4%2Asqrt%283%2Ax%2B4%29+%2B+3%2Ax+%2B+4\"$
\n" ); document.write( "which becomes
\n" ); document.write( " $\"x%2B2+=+8+%2B+3%2Ax+-+4%2Asqrt%283%2Ax%2B4%29\"$
\n" ); document.write( "subtracting 8 and 3*x from both sides of the equation and it becomes
\n" ); document.write( " $\"-2%2Ax+-+6+=+-4%2Asqrt%283%2Ax%2B4%29\"$
\n" ); document.write( "multiplying both sides of the eqution by (-1) and it becomes
\n" ); document.write( " $\"2%2Ax%2B6=4%2Asqrt%283%2Ax%2B4%29\"$
\n" ); document.write( "squaring both sides of the equation and it becomes
\n" ); document.write( " $\"4%2Ax%5E2+%2B+24%2Ax+%2B+36+=+16%2A%283%2Ax%2B4%29\"$
\n" ); document.write( "which becomes
\n" ); document.write( " $\"4%2Ax%5E2+-+24%2Ax+%2B+36+=+48%2Ax+%2B+64\"$
\n" ); document.write( "subtracting 48*x and 64 from both sides of the equation and it becomes
\n" ); document.write( " $\"4%2Ax%5E2+-+24%2Ax+-+28+=+0\"$
\n" ); document.write( "dividing both sides of the equation by 4 and it becomes
\n" ); document.write( " $\"x%5E2+-+6%2Ax+-+7+=+0\"$
\n" ); document.write( "this factors out into
\n" ); document.write( " $\"%28x-7%29%2A%28x%2B1%29+=+0\"$
\n" ); document.write( "x is either 7 or -1.
\n" ); document.write( "-----
\n" ); document.write( "substituting in original equation, x = 7 doesn't work, but x = -1 does.
\n" ); document.write( "answer is x = -1.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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