document.write( "Question 228745: what is the quadratic formula for 2x^2 - 11x - 1 = 0 \n" ); document.write( "
Algebra.Com's Answer #169736 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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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 \"2%2Ax%5E2-11%2Ax-1=0\" ( notice \"a=2\", \"b=-11\", and \"c=-1\")
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\n" ); document.write( " \"x+=+%28--11+%2B-+sqrt%28+%28-11%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29\" Plug in a=2, b=-11, and c=-1
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\n" ); document.write( " \"x+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29\" Negate -11 to get 11
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\n" ); document.write( " \"x+=+%2811+%2B-+sqrt%28+121-4%2A2%2A-1+%29%29%2F%282%2A2%29\" Square -11 to get 121 (note: remember when you square -11, you must square the negative as well. This is because \"%28-11%29%5E2=-11%2A-11=121\".)
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\n" ); document.write( " \"x+=+%2811+%2B-+sqrt%28+121%2B8+%29%29%2F%282%2A2%29\" Multiply \"-4%2A-1%2A2\" to get \"8\"
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\n" ); document.write( " \"x+=+%2811+%2B-+sqrt%28+129+%29%29%2F%282%2A2%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%2811+%2B-+sqrt%28129%29%29%2F%282%2A2%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+=+%2811+%2B-+sqrt%28129%29%29%2F4\" Multiply 2 and 2 to get 4
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%2811+%2B+sqrt%28129%29%29%2F4\" or \"x+=+%2811+-+sqrt%28129%29%29%2F4\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B11%2F4%2Bsqrt%28129%29%2F4\" or \"x=%2B11%2F4-sqrt%28129%29%2F4\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=11%2F4%2Bsqrt%28129%29%2F4\" or \"x=11%2F4-sqrt%28129%29%2F4\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=11%2F4%2Bsqrt%28129%29%2F4\" or \"x=11%2F4-sqrt%28129%29%2F4\"
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