document.write( "Question 291123: Hello\r
\n" ); document.write( "\n" ); document.write( "I'm really stuck on this question and would be very grateful if you could help me out.\r
\n" ); document.write( "\n" ); document.write( "QUESTION:Find the points of intersection of the line y=5x+13 with the circle \"+x%5E2%2By%5E2=13+\"\r
\n" ); document.write( "\n" ); document.write( "I'm not really sure how to approanch this question but have been attempting to solve it almost like a simultaneous equation by substitution:\r
\n" ); document.write( "\n" ); document.write( "\"+x%5E2%2B%285x%2B13%29%5E2=13+\"\r
\n" ); document.write( "\n" ); document.write( "This eventually gets me down to the quadratic:
\n" ); document.write( "\"+26x%5E2%2B130x%2B156=0+\"
\n" ); document.write( "simplified to \"+13x%5E2%2B65x%2B78=0+\"\r
\n" ); document.write( "\n" ); document.write( "This is all probably wrong but even if I am right I don't know where to go from here...\r
\n" ); document.write( "\n" ); document.write( "Please help!\r
\n" ); document.write( "\n" ); document.write( "Thanks ever so much,\r
\n" ); document.write( "\n" ); document.write( "From Katie
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Algebra.Com's Answer #210596 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
You're on the right track. I'll start where you left off.\r
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\n" ); document.write( "\n" ); document.write( "Let's solve \"+13x%5E2%2B65x%2B78=0+\" by use of the quadratic formula.\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"13%2Ax%5E2%2B65%2Ax%2B78=0\" ( notice \"a=13\", \"b=65\", and \"c=78\")
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\n" ); document.write( " \"x+=+%28-65+%2B-+sqrt%28+%2865%29%5E2-4%2A13%2A78+%29%29%2F%282%2A13%29\" Plug in a=13, b=65, and c=78
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\n" ); document.write( " \"x+=+%28-65+%2B-+sqrt%28+4225-4%2A13%2A78+%29%29%2F%282%2A13%29\" Square 65 to get 4225
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\n" ); document.write( " \"x+=+%28-65+%2B-+sqrt%28+4225%2B-4056+%29%29%2F%282%2A13%29\" Multiply \"-4%2A78%2A13\" to get \"-4056\"
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\n" ); document.write( " \"x+=+%28-65+%2B-+sqrt%28+169+%29%29%2F%282%2A13%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%28-65+%2B-+13%29%2F%282%2A13%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%28-65+%2B-+13%29%2F26\" Multiply 2 and 13 to get 26
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%28-65+%2B+13%29%2F26\" or \"x+=+%28-65+-+13%29%2F26\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-65+%2B+13%29%2F26\"
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\n" ); document.write( " \"x=-52%2F26\" Add the terms in the numerator
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\n" ); document.write( " \"x=-2\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=-2\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-65+-+13%29%2F26\"
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\n" ); document.write( " \"x=-78%2F26\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-3\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-3\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=-2\" or \"x=-3\"
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\n" ); document.write( "\n" ); document.write( "Now plug each of these solutions into \"y=5x%2B13\" to find the corresponding 'y' coordinates of the intersections. \r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-2\", then \"y=5x%2B13=5%28-2%29%2B13=-10%2B13=3\" giving us the point (-2,3)\r
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\n" ); document.write( "\n" ); document.write( "Also, when \"x=-3\", then \"y=5x%2B13=5%28-3%29%2B13=-15%2B13=-2\" giving us the point (-3,-2)\r
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\n" ); document.write( "\n" ); document.write( "So the two points of intersection are (-2,3) and (-3,-2)\r
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