document.write( "Question 1057311: This involves negative exponents and \"equations quadratic in form.\" The equation is:
\n" ); document.write( "x^-4 - 10^-2 + 9 = 0 (those are negative exponents: x to the negative fourth power, etc.)
\n" ); document.write( "To make solving easier, a substitution is used. Let u = x^-2, and rewrite the original equation as a quadratic equation:
\n" ); document.write( "u^2 - 10u + 9 = 0
\n" ); document.write( "Factor: (u-1)(u-9) = 0
\n" ); document.write( "Apply the zero-product principle: u-1 = 0 or u-9 = 0; so:
\n" ); document.write( " u = 1 or u = 9
\n" ); document.write( "Now replace u with x^-2 in each of the above equations:
\n" ); document.write( "x^-2 = 1 or x^-2 = 9.
\n" ); document.write( "Get rid of the negative exponents:
\n" ); document.write( "1/x^2 = 1 or 1/x^2 = 9\r
\n" ); document.write( "\n" ); document.write( "And now here is where I get confused. At this point, my professor writes this on the board as the next step:\r
\n" ); document.write( "\n" ); document.write( "x^2 = 1 or x^2 = 1/9\r
\n" ); document.write( "\n" ); document.write( "I have no idea how he got from the previous step to this step. \r
\n" ); document.write( "\n" ); document.write( "From here, he goes on to apply the square root property:\r
\n" ); document.write( "\n" ); document.write( "x = +-1 or x = +-1/3
\n" ); document.write( "This is the final answer.\r
\n" ); document.write( "\n" ); document.write( "So my question is:
\n" ); document.write( "How do we get from
\n" ); document.write( "1/x^2 = 1 or 1/x^2 = 9
\n" ); document.write( "to\r
\n" ); document.write( "\n" ); document.write( "x^2 = 1 or x^2 = 1/9
\n" ); document.write( "?
\n" ); document.write( "Thank you for any help you can give, and my apologies for the long question.
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #672365 by ikleyn(52813)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "So my question is:
\n" ); document.write( "How do we get from
\n" ); document.write( "1/x^2 = 1 or 1/x^2 = 9
\n" ); document.write( "to
\n" ); document.write( "x^2 = 1 or x^2 = 1/9
\n" ); document.write( "?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "If \"1%2Fx%5E2\" = 1, then multiply both sides by \"x%5E2\", and you will get 1 = \"x%5E2\", which is the same as \"x%5E2\" = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If \"1%2Fx%5E2\" = 9, then multiply both sides by \"x%5E2\", and you will get 1 = \"9x%5E2\", which is the same as \"9x%5E2\" = 1.\r\n" );
document.write( "\r\n" );
document.write( "Now divide both sides of the last equation by 9, and you will get \"x%5E2\" = \"1%2F9\".\r\n" );
document.write( "
\n" ); document.write( "
\n" );