document.write( "Question 240628: x^2-5x+35=0
\n" ); document.write( "it has no real solutions but what would be the irrational solution? \n" ); document.write( "
Algebra.Com's Answer #176312 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
This is a job for the quadratic formula. For
\n" ); document.write( "\"ax%5E2+%2B+bx+%2B+c+=+0\"
\n" ); document.write( "the solutions can be found with:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29\"

\n" ); document.write( "In your equation, \"x%5E2-5x%2B35\"
\n" ); document.write( "a = 1
\n" ); document.write( "b = -5
\n" ); document.write( "c = 35
\n" ); document.write( "So the solutions are:
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2+-+4%281%29%2835%29%29%29%2F%282%281%29%29\"
\n" ); document.write( "Simplifying inside the square root:
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%2825+-+4%281%29%2835%29%29%29%2F%282%281%29%29\"
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%2825+-+140%29%29%2F%282%281%29%29\"
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%28-115%29%29%2F%282%281%29%29\"
\n" ); document.write( "At this point, since there is a negative number in the square root, we know that the solutions will be complex (not irrational). For complex numbers we use \"i\" which stand for \"sqrt%28-1%29\":
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%28%28-1%29%28115%29%29%29%2F%282%281%29%29\"
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%28-1%29sqrt%28115%29%29%2F%282%281%29%29\"
\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+i%2Asqrt%28115%29%29%2F%282%281%29%29\"
\n" ); document.write( "Simplifying the rest we get:
\n" ); document.write( "\"x+=+%285+%2B-+i%2Asqrt%28115%29%29%2F2\"
\n" ); document.write( "Separating this into two terms and writing this in a+bi form we get:
\n" ); document.write( "\"x+=+5%2F2+%2B-+%28sqrt%28115%29%2F2%29i\"
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