document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462550>Question 462550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all real solutions of the equations : (x^2 +1)^2 - 18( x^2 +1) = -17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317083 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B1%29%5E2+-+18%28+x%5E2+%2B1%29+=+-17 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B1%29%5E2+-+18%28+x%5E2+%2B1%29+=+-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B2x%5E2+%2B1+-+18x%5E2+-1+=+-17 ALIGN=MIDDLE  ALT=\"x%5E4%2B2x%5E2+%2B1+-+18x%5E2+-1+=+-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-16x%5E2+%2B17=0 ALIGN=MIDDLE  ALT=\"x%5E4+-16x%5E2+%2B17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2+-16x%5E2+%2B17=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2+-16x%5E2+%2B17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...you can solve it as quadratic using quadratic formula, you will just have four solutions; both solutions as quadratic equation you will take positive i negative value of their square root\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16%2Ax%2B17=0 ALIGN=MIDDLE  ALT=\"x%5E2-16%2Ax%2B17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-16 ALIGN=MIDDLE  ALT=\"b=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=17 ALIGN=MIDDLE  ALT=\"c=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-16, and c=17<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -16 to get 16<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+256-4%2A1%2A17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256-4%2A1%2A17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -16 to get 256  (note: remember when you square -16, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%29%5E2=-16%2A-16=256 ALIGN=MIDDLE  ALT=\"%28-16%29%5E2=-16%2A-16=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+256%2B-68+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256%2B-68+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A17%2A1 ALIGN=MIDDLE  ALT=\"-4%2A17%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-68 ALIGN=MIDDLE  ALT=\"-68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+188+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+188+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+2%2Asqrt%2847%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+2%2Asqrt%2847%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+2%2Asqrt%2847%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+2%2Asqrt%2847%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B+2%2Asqrt%2847%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B+2%2Asqrt%2847%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+-+2%2Asqrt%2847%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2816+-+2%2Asqrt%2847%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B16%2F2%2B2%2Asqrt%2847%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B16%2F2%2B2%2Asqrt%2847%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B16%2F2-2%2Asqrt%2847%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B16%2F2-2%2Asqrt%2847%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2Bsqrt%2847%29 ALIGN=MIDDLE  ALT=\"x=8%2Bsqrt%2847%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-sqrt%2847%29 ALIGN=MIDDLE  ALT=\"x=8-sqrt%2847%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2Bsqrt%2847%29 ALIGN=MIDDLE  ALT=\"x=8%2Bsqrt%2847%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-sqrt%2847%29 ALIGN=MIDDLE  ALT=\"x=8-sqrt%2847%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So yoursolutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%288%2B%28sqrt%2847%29%29%29+ ALIGN=MIDDLE  ALT=\"x=sqrt%288%2B%28sqrt%2847%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%288-%28sqrt%2847%29%29%29 ALIGN=MIDDLE  ALT=\"x=sqrt%288-%28sqrt%2847%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%288%2B6.8556546%29+ ALIGN=MIDDLE  ALT=\"x=sqrt%288%2B6.8556546%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%288-6.8556546%29 ALIGN=MIDDLE  ALT=\"x=sqrt%288-6.8556546%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2814.8556546%29+ ALIGN=MIDDLE  ALT=\"x=sqrt%2814.8556546%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%281.1443454%29 ALIGN=MIDDLE  ALT=\"x=sqrt%281.1443454%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.8543 ALIGN=MIDDLE  ALT=\"x=3.8543\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.06974 ALIGN=MIDDLE  ALT=\"x=1.06974\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.8543 ALIGN=MIDDLE  ALT=\"x=3.8543\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.8543 ALIGN=MIDDLE  ALT=\"x=-3.8543\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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