document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709890>Question 709890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve x^4+x^2-30 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436810 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=436810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve, let's first factor our expression:  x^4 + x^2 - 30.  What two numbers, when multiplied, give us -30, and when added, give us 1?  Let's find out:\r<BR>\n" );
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document.write( "-1 x 30 = -30; -1 + 30 = 29  NO\r<BR>\n" );
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document.write( "-2 x 15 = -30; -2 + 15 = 13  NO\r<BR>\n" );
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document.write( "-3 x 10 = -30; -3 + 10 = 7  NO\r<BR>\n" );
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document.write( "-5 x 6 = -30; -5 + 6 = 1  YES!!\r<BR>\n" );
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document.write( "Since -5 and 6 work, we will now factor our expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5%29%28x%5E2+%2B+6%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+5%29%28x%5E2+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find x, we will set each of these factors equal to 0:\r<BR>\n" );
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document.write( "x^2 - 5 = 0 =\r<BR>\n" );
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document.write( "Add 5 to both sides:\r<BR>\n" );
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document.write( "x^2 = 5\r<BR>\n" );
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document.write( "Finally, take the square root of both sides, remembering to add a +- sign.  This gives us \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B-sqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+%2B-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, take our other factor and set to zero:\r<BR>\n" );
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document.write( "x^2 + 6 = 0\r<BR>\n" );
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document.write( "Subtract 6 from both sides, giving us\r<BR>\n" );
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document.write( "x^2 = -6\r<BR>\n" );
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document.write( "Take the square root of both sides, remembering to add a +- sign to the right side equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B-sqrt%28-6%29 ALIGN=MIDDLE  ALT=\"x+=+%2B-sqrt%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-6%29+=+i%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%28-6%29+=+i%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Our final answer is x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%285%29 ALIGN=MIDDLE  ALT=\"-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"-i%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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