document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195697>Question 195697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7x^2-16x-28=0\r<BR>\n" );
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document.write( "11x^2=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146762 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=146762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2-16x-28=0 ALIGN=MIDDLE  ALT=\"7x%5E2-16x-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\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=7 ALIGN=MIDDLE  ALT=\"a=7\"   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=-28 ALIGN=MIDDLE  ALT=\"c=-28\"   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-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7 ALIGN=MIDDLE  ALT=\"a=7\"   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=-28 ALIGN=MIDDLE  ALT=\"c=-28\"   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+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   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+=+%2816+%2B-+sqrt%28+256-4%287%29%28-28%29+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256-4%287%29%28-28%29+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   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+=+%2816+%2B-+sqrt%28+256--784+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256--784+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%287%29%28-28%29 ALIGN=MIDDLE  ALT=\"4%287%29%28-28%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-784 ALIGN=MIDDLE  ALT=\"-784\"   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+=+%2816+%2B-+sqrt%28+256%2B784+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256%2B784+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28256--784%29 ALIGN=MIDDLE  ALT=\"sqrt%28256--784%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28256%2B784%29 ALIGN=MIDDLE  ALT=\"sqrt%28256%2B784%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+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%282%287%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%282%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=784 ALIGN=MIDDLE  ALT=\"784\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1040 ALIGN=MIDDLE  ALT=\"1040\"   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+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%2814%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%2814%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=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   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+=+%2816+%2B-+4%2Asqrt%2865%29%29%2F%2814%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+4%2Asqrt%2865%29%29%2F%2814%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+=+%2816%2B4%2Asqrt%2865%29%29%2F%2814%29 ALIGN=MIDDLE  ALT=\"x+=+%2816%2B4%2Asqrt%2865%29%29%2F%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816-4%2Asqrt%2865%29%29%2F%2814%29 ALIGN=MIDDLE  ALT=\"x+=+%2816-4%2Asqrt%2865%29%29%2F%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29 ALIGN=MIDDLE  ALT=\"x+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288-2%2Asqrt%2865%29%29%2F%287%29 ALIGN=MIDDLE  ALT=\"x+=+%288-2%2Asqrt%2865%29%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce  \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+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29 ALIGN=MIDDLE  ALT=\"x+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288-2%2Asqrt%2865%29%29%2F%287%29 ALIGN=MIDDLE  ALT=\"x+=+%288-2%2Asqrt%2865%29%29%2F%287%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=3.446 ALIGN=MIDDLE  ALT=\"x=3.446\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.161 ALIGN=MIDDLE  ALT=\"x=-1.161\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%5E2=8 ALIGN=MIDDLE  ALT=\"11x%5E2=8\"   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=x%5E2=8%2F11 ALIGN=MIDDLE  ALT=\"x%5E2=8%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   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=%22%22%2B-sqrt%288%2F11%29 ALIGN=MIDDLE  ALT=\"x=%22%22%2B-sqrt%288%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%288%2F11%29 ALIGN=MIDDLE  ALT=\"x=sqrt%288%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%288%2F11%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%288%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the \"plus/minus\" to form two equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2Asqrt%2822%29%29%2F11 ALIGN=MIDDLE  ALT=\"x=%282%2Asqrt%2822%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%282%2Asqrt%2822%29%29%2F11 ALIGN=MIDDLE  ALT=\"x=-%282%2Asqrt%2822%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify the square root.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2Asqrt%2822%29%29%2F11 ALIGN=MIDDLE  ALT=\"x=%282%2Asqrt%2822%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%282%2Asqrt%2822%29%29%2F11 ALIGN=MIDDLE  ALT=\"x=-%282%2Asqrt%2822%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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