document.write( "Question 695868: solve over the set of complex numbers
\n" ); document.write( "(x+5)^2=-36 (given)
\n" ); document.write( "if I work it out I get x^2-10x+61=0
\n" ); document.write( "but now what, it won't foil,
\n" ); document.write( "x^2-10x+25=-36
\n" ); document.write( "x^2-10x+25= -61+25 completing the square gets me right back where I started... \n" ); document.write( "

Algebra.Com's Answer #428660 by KMST(5328) $\"\"$ $\"About$

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To solve a quadratic equation for complex solutions, you work just as you do for real solutions,
\n" ); document.write( "except that you go further than the point where you would say the equation has no real solutions,
\n" ); document.write( "because a negative number cannot be the square of a real number,
\n" ); document.write( "but it is the square of a complex number.
\n" ); document.write( "
\n" ); document.write( " $\"%28x%2B5%29%5E2=-36\"$ <--> $\"%28x%2B5%29%5E2=%28-1%29%286%5E2%29\"$
\n" ); document.write( "The only real (and complex) numbers that squared equal $\"36=6%5E2\"$ are $\"-6\"$ and $\"6\"$
\n" ); document.write( "The only complex numbers that squared equal $\"-1\"$ are $\"-i\"$ and $\"i\"$
\n" ); document.write( "So, the only complex numbers that squared equal $\"-36=%28-1%29%286%5E2%29\"$ are $\"-6i\"$ and $\"6i\"$ .
\n" ); document.write( "So, either $\"x%2B5=-6i\"$ <--> $\"highlight%28x=-5-6i%29\"$ ,
\n" ); document.write( "or $\"x%2B5=6i\"$ <--> $\"highlight%28x=-5%2B6i%29\"$ \n" ); document.write( "

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