document.write( "Question 766915: find all complex solutions of 2x^2-x+6=0thanks \n" ); document.write( "
Algebra.Com's Answer #467313 by MathLover1(20849)\"\" \"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-x%2B6=0\" ( notice \"a=2\", \"b=-1\", and \"c=6\")
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\n" ); document.write( " \"x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A6+%29%29%2F%282%2A2%29\" Plug in a=2, b=-1, and c=6
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\n" ); document.write( " \"x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A6+%29%29%2F%282%2A2%29\" Negate -1 to get 1
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\n" ); document.write( " \"x+=+%281+%2B-+sqrt%28+1-4%2A2%2A6+%29%29%2F%282%2A2%29\" Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because \"%28-1%29%5E2=-1%2A-1=1\".)
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\n" ); document.write( " \"x+=+%281+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A2%29\" Multiply \"-4%2A6%2A2\" to get \"-48\"
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\n" ); document.write( " \"x+=+%281+%2B-+sqrt%28+-47+%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+=+%281+%2B-+i%2Asqrt%2847%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+=+%281+%2B-+i%2Asqrt%2847%29%29%2F%284%29\" Multiply 2 and 2 to get 4
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\n" ); document.write( " After simplifying, the quadratic has roots of
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\n" ); document.write( " \"x=1%2F4%2Bsqrt%2847%29%2F4%2Ai\" or \"x=1%2F4-sqrt%2847%29%2F4%2Ai\"
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