document.write( "Question 111852: Find the roots of 2x to the second power-5x+1=0 \n" ); document.write( "
Algebra.Com's Answer #81583 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%5E2-5%2Ax%2B1=0\" ( notice \"a=2\", \"b=-5\", and \"c=1\")
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\n" ); document.write( " \"x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29\" Plug in a=2, b=-5, and c=1
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\n" ); document.write( " \"x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29\" Negate -5 to get 5
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\n" ); document.write( " \"x+=+%285+%2B-+sqrt%28+25-4%2A2%2A1+%29%29%2F%282%2A2%29\" Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because \"%28-5%29%5E2=-5%2A-5=25\".)
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\n" ); document.write( " \"x+=+%285+%2B-+sqrt%28+25%2B-8+%29%29%2F%282%2A2%29\" Multiply \"-4%2A1%2A2\" to get \"-8\"
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\n" ); document.write( " \"x+=+%285+%2B-+sqrt%28+17+%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+=+%285+%2B-+sqrt%2817%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+=+%285+%2B-+sqrt%2817%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+=+%285+%2B+sqrt%2817%29%29%2F4\" or \"x+=+%285+-+sqrt%2817%29%29%2F4\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B5%2F4%2Bsqrt%2817%29%2F4\" or \"x=%2B5%2F4-sqrt%2817%29%2F4\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=5%2F4%2Bsqrt%2817%29%2F4\" or \"x=5%2F4-sqrt%2817%29%2F4\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=5%2F4%2Bsqrt%2817%29%2F4\" or \"x=5%2F4-sqrt%2817%29%2F4\"
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