document.write( "Question 270407: one leg of a right triangle exceeds the other leg by four inches. the hypotenuse is 10 inches. find the length of the shorter leg of the right triangle . \n" ); document.write( "
Algebra.Com's Answer #198143 by Greenfinch(383)\"\" \"About 
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By Pythagoras
\n" ); document.write( "x^2 + (x + 4)^2 = 100
\n" ); document.write( "2x^2 + 8x + 16 = 100
\n" ); document.write( "x^2 + 4x - 42 = 0\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B4x%2B-42+=+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=%284%29%5E2-4%2A1%2A-42=184\".
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\n" ); document.write( " Discriminant d=184 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-4%2B-sqrt%28+184+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+184+%29%29%2F2%5C1+=+4.78232998312527\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%284%29-sqrt%28+184+%29%29%2F2%5C1+=+-8.78232998312527\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B4x%2B-42\" can be factored:
\n" ); document.write( " \"1x%5E2%2B4x%2B-42+=+1%28x-4.78232998312527%29%2A%28x--8.78232998312527%29\"
\n" ); document.write( " Again, the answer is: 4.78232998312527, -8.78232998312527.\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%2B4%2Ax%2B-42+%29\"

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