document.write( "Question 192279This question is from textbook Elementary and intermediate algebra
\n" ); document.write( ": b^4 + 13b^2 + 36 = 0 find all real and imaginary solutions to the equation \n" ); document.write( "

Algebra.Com's Answer #144311 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for b:
\n" ); document.write( " $\"b%5E4%2B13b%5E2%2B36+=+0\"$ Rewrite this as a quadratic equation:
\n" ); document.write( " $\"%28b%5E2%29%5E2%2B13%28b%5E2%29+%2B+36+=+0\"$ Factor:
\n" ); document.write( " $\"%28b%5E2%2B4%29%28b%5E2%2B9%29+=+0\"$ Apply the zero product rule:
\n" ); document.write( " $\"b%5E2%2B4+=+0\"$ or $\"b%5E2%2B9+=+0\"$ so...
\n" ); document.write( " $\"b%5E2+=+-4\"$ or $\"b%5E2+=+-9\"$
\n" ); document.write( " $\"b%5E2+=+-4\"$ Take the square root of both sides.
\n" ); document.write( " $\"b+=+sqrt%28-4%29\"$ or $\"b+=+-sqrt%28-4%29\"$ these can be written as:
\n" ); document.write( " $\"b+=+2i\"$ or $\"b+=+-2i\"$ where $\"i+=+sqrt%28-1%29\"$
\n" ); document.write( " $\"b%5E2+=+-9\"$ Take the square root of both sides.
\n" ); document.write( " $\"b+=+sqrt%28-9%29\"$ or $\"b+=+-sqrt%28-9%29\"$ these can be written as:
\n" ); document.write( " $\"b+=+3i\"$ or $\"b+=+-3i\"$
\n" ); document.write( "The roots are:
\n" ); document.write( " $\"b+=+2i\"$
\n" ); document.write( " $\"b+=+-2i\"$
\n" ); document.write( " $\"b+=+3i\"$
\n" ); document.write( " $\"b+=+-3i\"$ \n" ); document.write( "

\n" );