document.write( "Question 90400: Number problems. Find two consecutive positive integers such that the sum of
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Algebra.Com's Answer #65611 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E2%2B%28x%2B1%29%5E2=85\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2Bx%5E2%2B2x%2B1=85\" Foil\r
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\n" ); document.write( "\n" ); document.write( "\"2x%5E2%2B2x%2B1=85\" Combine like terms\r
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\n" ); document.write( "\n" ); document.write( "\"2x%5E2%2B2x-84=0\" Subtract 85 from both sides\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x:\r
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\n" ); document.write( "\n" ); document.write( "Starting with the general quadratic\r
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\n" ); document.write( "\n" ); document.write( "\"ax%5E2%2Bbx%2Bc=0\"\r
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\n" ); document.write( "\n" ); document.write( "the general solution using the quadratic equation is:\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"\r
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\n" ); document.write( "\n" ); document.write( "So lets solve \"2%2Ax%5E2%2B2%2Ax-84=0\" ( notice \"a=2\", \"b=2\", and \"c=-84\")\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A2%2A-84+%29%29%2F%282%2A2%29\" Plug in a=2, b=2, and c=-84\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+4-4%2A2%2A-84+%29%29%2F%282%2A2%29\" Square 2 to get 4 \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+4%2B672+%29%29%2F%282%2A2%29\" Multiply \"-4%2A-84%2A2\" to get \"672\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+676+%29%29%2F%282%2A2%29\" Combine like terms in the radicand (everything under the square root)\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+26%29%2F%282%2A2%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+26%29%2F4\" Multiply 2 and 2 to get 4\r
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\n" ); document.write( "\n" ); document.write( "So now the expression breaks down into two parts\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B+26%29%2F4\" or \"x+=+%28-2+-+26%29%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "Lets look at the first part:\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-2+%2B+26%29%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=24%2F4\" Add the terms in the numerator\r
\n" ); document.write( "\n" ); document.write( "\"x=6\" Divide\r
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\n" ); document.write( "\n" ); document.write( "So one answer is\r
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\n" ); document.write( "\n" ); document.write( "Now lets look at the second part:\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-2+-+26%29%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=-28%2F4\" Subtract the terms in the numerator\r
\n" ); document.write( "\n" ); document.write( "\"x=-7\" Divide\r
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\n" ); document.write( "\n" ); document.write( "So another answer is\r
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\n" ); document.write( "\n" ); document.write( "Since we only care about the positive numbers, our solution is:\r
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\n" ); document.write( "\n" ); document.write( "So our second number is \r
\n" ); document.write( "\n" ); document.write( "\"6%2B1=7\"\r
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\n" ); document.write( "\n" ); document.write( "which means our numbers are\r
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