document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220696>Question 220696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a quadratic Equation  2x^2=90 <BR>\n" );
document.write( "How do i use the quadratic formula if there is no middle term?\r<BR>\n" );
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document.write( "Thank you<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 #165616 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=165616\">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=2x%5E2=90 ALIGN=MIDDLE  ALT=\"2x%5E2=90\"   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%5E2-90=0 ALIGN=MIDDLE  ALT=\"2x%5E2-90=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 90 from both sides\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( "  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=2%2Ax%5E2-90=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-90=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: since the polynomial does not have an \"x\" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2%2B0%2Ax-90=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B0%2Ax-90=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   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=-90 ALIGN=MIDDLE  ALT=\"c=-90\"   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+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A2%2A-90+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A2%2A-90+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=0, and c=-90<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B-+sqrt%28+0-4%2A2%2A-90+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0-4%2A2%2A-90+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 0 to get 0  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B-+sqrt%28+0%2B720+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0%2B720+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-90%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-90%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720 ALIGN=MIDDLE  ALT=\"720\"   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+=+%280+%2B-+sqrt%28+720+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+720+%29%29%2F%282%2A2%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+=+%280+%2B-+12%2Asqrt%285%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+12%2Asqrt%285%29%29%2F%282%2A2%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+=+%280+%2B-+12%2Asqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+12%2Asqrt%285%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4<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+=+%280+%2B+12%2Asqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B+12%2Asqrt%285%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+-+12%2Asqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%280+-+12%2Asqrt%285%29%29%2F4\"   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=0%2F4%2B12%2Asqrt%285%29%2F4 ALIGN=MIDDLE  ALT=\"x=0%2F4%2B12%2Asqrt%285%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2F4-12%2Asqrt%285%29%2F4 ALIGN=MIDDLE  ALT=\"x=0%2F4-12%2Asqrt%285%29%2F4\"   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=0%2B3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=0%2B3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0-3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=0-3%2Asqrt%285%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=0%2B3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=0%2B3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0-3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=0-3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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