document.write( "Question 677510: -5(n-3)^2=10 \n" ); document.write( "
Algebra.Com's Answer #420937 by edjones(8007)\"\" \"About 
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-5(n-3)^2=10
\n" ); document.write( "(n-3)^2=-2
\n" ); document.write( "n^2-6n+9=-2
\n" ); document.write( "n^2-6n+11=0
\n" ); document.write( "n=3-sqrt(2)i, n=3+sqt(2)i
\n" ); document.write( "see below.
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\n" ); document.write( "Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-6x%2B11+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-6%29%5E2-4%2A1%2A11=-8\".
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\n" ); document.write( " The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -8 is + or - \"sqrt%28+8%29+=+2.82842712474619\".
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\n" ); document.write( " The solution is
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\n" ); document.write( " Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B11+%29\"
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