document.write( "Question 419876: Please help me solve \"lnx%2Bln%28x%2B3%29=1\" \n" ); document.write( "
Algebra.Com's Answer #293503 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
\"lnx%2Bln%28x%2B3%29=1\"
\n" ); document.write( "\"ln+x%28x%2B3%29=1\"
\n" ); document.write( "\"x%28x%2B3%29=+e%5E1\"
\n" ); document.write( "\"x%5E2%2B3x=+2.718\"
\n" ); document.write( "\"x%5E2%2B3x-2.718=+0\"
\n" ); document.write( "Solve by applying the quadratic formula to give:
\n" ); document.write( "x = {0.729, -3.729}
\n" ); document.write( "we can throw out the negative solution leaving:
\n" ); document.write( "x = 0.729
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\n" ); document.write( "Details of quadratic formula follows:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B3x%2B-2.718281828+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%283%29%5E2-4%2A1%2A-2.718281828=19.873127312\".
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\n" ); document.write( " Discriminant d=19.873127312 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-3%2B-sqrt%28+19.873127312+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+19.873127312+%29%29%2F2%5C1+=+0.728964294913671\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%283%29-sqrt%28+19.873127312+%29%29%2F2%5C1+=+-3.72896429491367\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B3x%2B-2.718281828\" can be factored:
\n" ); document.write( " \"1x%5E2%2B3x%2B-2.718281828+=+1%28x-0.728964294913671%29%2A%28x--3.72896429491367%29\"
\n" ); document.write( " Again, the answer is: 0.728964294913671, -3.72896429491367.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-2.718281828+%29\"

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