document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96856>Question 96856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2-48=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70477 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=70477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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%5E2-4%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;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48=0 ALIGN=MIDDLE  ALT=\"x%5E2-48=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=x%5E2%2B0%2Ax-48=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B0%2Ax-48=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=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=-48 ALIGN=MIDDLE  ALT=\"c=-48\"   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+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=0, and c=-48\r<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%2A1%2A-48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0-4%2A1%2A-48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 0 to get 0  \r<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%2B192+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+0%2B192+%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%2A-48%2A1 ALIGN=MIDDLE  ALT=\"-4%2A-48%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   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+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B-+8%2Asqrt%283%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+8%2Asqrt%283%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>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B-+8%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B-+8%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+%2B+8%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%280+%2B+8%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%280+-+8%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%280+-+8%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now 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%2F2%2B8%2Asqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"x=0%2F2%2B8%2Asqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2F2-8%2Asqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"x=0%2F2-8%2Asqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.92820323027551 ALIGN=MIDDLE  ALT=\"x=6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.92820323027551 ALIGN=MIDDLE  ALT=\"x=-6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.92820323027551 ALIGN=MIDDLE  ALT=\"x=6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.92820323027551 ALIGN=MIDDLE  ALT=\"x=-6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48 ALIGN=MIDDLE  ALT=\"x%5E2-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-16.9282032302755%2C+16.9282032302755%2C+-16.9282032302755%2C+16.9282032302755%2C1%2Ax%5E2%2B0%2Ax%2B-48%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.92820323027551 ALIGN=MIDDLE  ALT=\"x=6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.92820323027551 ALIGN=MIDDLE  ALT=\"x=-6.92820323027551\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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