document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151501>Question 151501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For about what value(s) of x does g(x)=k(x) if g(x)=2x^2 -8 and k(x) =-x^2 -2?\r<BR>\n" );
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document.write( "x~ +or-2<BR>\n" );
document.write( "x~ +or-2.3<BR>\n" );
document.write( "x~ 1.4<BR>\n" );
document.write( "x~ +or- 1.4<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111358 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2x%5E2+-8 ALIGN=MIDDLE  ALT=\"g%28x%29=2x%5E2+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28x%29+=-x%5E2+-2 ALIGN=MIDDLE  ALT=\"k%28x%29+=-x%5E2+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=k%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29=k%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-8=-x%5E2+-2 ALIGN=MIDDLE  ALT=\"2x%5E2+-8=-x%5E2+-2\"   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=2x%5E2-8=-x%5E2-2 ALIGN=MIDDLE  ALT=\"2x%5E2-8=-x%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8%2B1x%5E2%2B2=0 ALIGN=MIDDLE  ALT=\"2x%5E2-8%2B1x%5E2%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides. Add 2 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-6=0 ALIGN=MIDDLE  ALT=\"3x%5E2-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<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%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%283%29%28-6%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%280%29+%2B-+sqrt%28+%280%29%5E2-4%283%29%28-6%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   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+=+%28-0+%2B-+sqrt%28+0-4%283%29%28-6%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+sqrt%28+0-4%283%29%28-6%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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=x+=+%28-0+%2B-+sqrt%28+0--72+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+sqrt%28+0--72+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%29%28-6%29 ALIGN=MIDDLE  ALT=\"4%283%29%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72 ALIGN=MIDDLE  ALT=\"-72\"   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+=+%28-0+%2B-+sqrt%28+0%2B72+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+sqrt%28+0%2B72+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280--72%29 ALIGN=MIDDLE  ALT=\"sqrt%280--72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280%2B72%29 ALIGN=MIDDLE  ALT=\"sqrt%280%2B72%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+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   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+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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+=+%28-0+%2B-+6%2Asqrt%282%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0+%2B-+6%2Asqrt%282%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-0%29%2F%286%29+%2B-+%286%2Asqrt%282%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%28-0%29%2F%286%29+%2B-+%286%2Asqrt%282%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0+%2B-+sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+0+%2B-+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.414 ALIGN=MIDDLE  ALT=\"x=1.414\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.414 ALIGN=MIDDLE  ALT=\"x=-1.414\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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