document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91107>Question 91107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this, 5x^2 + 14x = -3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66135 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=66135\">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=5x%5E2+%2B+14x+=+-3 ALIGN=MIDDLE  ALT=\"5x%5E2+%2B+14x+=+-3\"   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=5x%5E2+%2B+14x+%2B3=0 ALIGN=MIDDLE  ALT=\"5x%5E2+%2B+14x+%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides\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( "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=5%2Ax%5E2%2B14%2Ax%2B3=0 ALIGN=MIDDLE  ALT=\"5%2Ax%5E2%2B14%2Ax%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=14 ALIGN=MIDDLE  ALT=\"b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   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+=+%28-14+%2B-+sqrt%28+%2814%29%5E2-4%2A5%2A3+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+sqrt%28+%2814%29%5E2-4%2A5%2A3+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=5, b=14, and c=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-14+%2B-+sqrt%28+196-4%2A5%2A3+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+sqrt%28+196-4%2A5%2A3+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 14 to get 196  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-14+%2B-+sqrt%28+196%2B-60+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+sqrt%28+196%2B-60+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A3%2A5 ALIGN=MIDDLE  ALT=\"-4%2A3%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60 ALIGN=MIDDLE  ALT=\"-60\"   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+=+%28-14+%2B-+sqrt%28+136+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+sqrt%28+136+%29%29%2F%282%2A5%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+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F%282%2A5%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+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B-+2%2Asqrt%2834%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 5 to get 10\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+=+%28-14+%2B+2%2Asqrt%2834%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%28-14+%2B+2%2Asqrt%2834%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-14+-+2%2Asqrt%2834%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%28-14+-+2%2Asqrt%2834%29%29%2F10\"   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=-14%2F10%2B2%2Asqrt%2834%29%2F10 ALIGN=MIDDLE  ALT=\"x=-14%2F10%2B2%2Asqrt%2834%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-14%2F10-2%2Asqrt%2834%29%2F10 ALIGN=MIDDLE  ALT=\"x=-14%2F10-2%2Asqrt%2834%29%2F10\"   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=-7+%2F+5%2Bsqrt%2834%29%2F5 ALIGN=MIDDLE  ALT=\"x=-7+%2F+5%2Bsqrt%2834%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7+%2F+5-sqrt%2834%29%2F5 ALIGN=MIDDLE  ALT=\"x=-7+%2F+5-sqrt%2834%29%2F5\"   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=-0.23380962103094 ALIGN=MIDDLE  ALT=\"x=-0.23380962103094\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.56619037896906 ALIGN=MIDDLE  ALT=\"x=-2.56619037896906\"   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=-0.23380962103094 ALIGN=MIDDLE  ALT=\"x=-0.23380962103094\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.56619037896906 ALIGN=MIDDLE  ALT=\"x=-2.56619037896906\"   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=5%2Ax%5E2%2B14%2Ax%2B3 ALIGN=MIDDLE  ALT=\"5%2Ax%5E2%2B14%2Ax%2B3\"   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+-12.5661903789691%2C+9.76619037896906%2C+-12.5661903789691%2C+9.76619037896906%2C5%2Ax%5E2%2B14%2Ax%2B3%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=-0.23380962103094 ALIGN=MIDDLE  ALT=\"x=-0.23380962103094\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.56619037896906 ALIGN=MIDDLE  ALT=\"x=-2.56619037896906\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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