document.write( "Question 58099This question is from textbook Algebra 2
\n" ); document.write( ": \"log10%28a%29%2Blog10%28a%2B21%29=2\" \n" ); document.write( "
Algebra.Com's Answer #39759 by hayek(51)\"\" \"About 
You can put this solution on YOUR website!
Using: \"log10%28a%29%2Blog10%28b%29+=+log10%28a%2Ab%29\"\r
\n" ); document.write( "\n" ); document.write( "\"log10%28a%2A%28a%2B21%29%29=2\"
\n" ); document.write( "\"log10%28a%5E2%2B21a%29%29=2\"
\n" ); document.write( "\"10%5E2=%28a%5E2%2B21a%29\"
\n" ); document.write( "\"a%5E2%2B21a-100=0\"
\n" ); document.write( "Using quadratic formula, taking the positive solution (see below) \"a=4\"
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"a0%5E2%2Bb0%2Bc=0\" (in our case \"10%5E2%2B210%2B-100+=+0\") has the following solutons:
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\n" ); document.write( " \"0%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=%2821%29%5E2-4%2A1%2A-100=841\".
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\n" ); document.write( " Discriminant d=841 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-21%2B-sqrt%28+841+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"0%5B1%5D+=+%28-%2821%29%2Bsqrt%28+841+%29%29%2F2%5C1+=+4\"
\n" ); document.write( " \"0%5B2%5D+=+%28-%2821%29-sqrt%28+841+%29%29%2F2%5C1+=+-25\"
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\n" ); document.write( " Quadratic expression \"10%5E2%2B210%2B-100\" can be factored:
\n" ); document.write( " \"10%5E2%2B210%2B-100+=+1%280-4%29%2A%280--25%29\"
\n" ); document.write( " Again, the answer is: 4, -25.\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%2B21%2Ax%2B-100+%29\"

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