document.write( "Question 177254: Two numbers differ by 6. if the numbers are squared and then added, the result is 146. What are the numbers? \n" ); document.write( "
Algebra.Com's Answer #132330 by jim_thompson5910(35256)\"\" \"About 
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\"Two numbers differ by 6\" translates to \"x-y=6\". If we solve for \"y\", we get \"y=x-6\"\r
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\n" ); document.write( "\n" ); document.write( "\"if the numbers are squared and then added, the result is 146\" means that \"x%5E2%2By%5E2=146\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2By%5E2=146\" Start with the second equation.\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B%28x-6%29%5E2=146\" Plug in \"y=x-6\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2Bx%5E2-12x%2B36=146\" FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2Bx%5E2-12x%2B36-146=0\" Subtract 146 from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"2x%5E2-12x-110=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"ax%5E2%2Bbx%2Bc\" where \"a=2\", \"b=-12\", and \"c=-110\"\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( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%282%29%28-110%29+%29%29%2F%282%282%29%29\" Plug in \"a=2\", \"b=-12\", and \"c=-110\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%282%29%28-110%29+%29%29%2F%282%282%29%29\" Negate \"-12\" to get \"12\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+144-4%282%29%28-110%29+%29%29%2F%282%282%29%29\" Square \"-12\" to get \"144\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+144--880+%29%29%2F%282%282%29%29\" Multiply \"4%282%29%28-110%29\" to get \"-880\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+144%2B880+%29%29%2F%282%282%29%29\" Rewrite \"sqrt%28144--880%29\" as \"sqrt%28144%2B880%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+1024+%29%29%2F%282%282%29%29\" Add \"144\" to \"880\" to get \"1024\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+sqrt%28+1024+%29%29%2F%284%29\" Multiply \"2\" and \"2\" to get \"4\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B-+32%29%2F%284%29\" Take the square root of \"1024\" to get \"32\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2812+%2B+32%29%2F%284%29\" or \"x+=+%2812+-+32%29%2F%284%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2844%29%2F%284%29\" or \"x+=++%28-20%29%2F%284%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+11\" or \"x+=+-5\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the first numbers are either \"x+=+11\" or \"x+=+-5\" \r
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\n" ); document.write( "\n" ); document.write( "\"y=x-6\" Go back to the isolated equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=11-6\" Plug in the first solution \"x=11\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=5\" Subtract\r
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\n" ); document.write( "\n" ); document.write( "So when \"x+=+11\", then \"y=5\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=x-6\" Go back to the isolated equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=-5-6\" Plug in the first solution \"x=11\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-11\" Subtract\r
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\n" ); document.write( "\n" ); document.write( "So when \"x+=+-5\", then \"y=-11\"\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So this means that the two numbers are\r
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\n" ); document.write( "\n" ); document.write( "11 and 5\r
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\n" ); document.write( "\n" ); document.write( "OR\r
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\n" ); document.write( "\n" ); document.write( "-5 and -11 \n" ); document.write( "
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