document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132297>Question 132297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help?\r<BR>\n" );
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document.write( "Solve 3x^2-5x-7=0 <BR>\n" );
document.write( "Find x intercepts of f(x)=3x^2-5x-7\r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96650 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=96650\">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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2-5%2Ax-7=0 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2-5%2Ax-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-7 ALIGN=MIDDLE  ALT=\"c=-7\"   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--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=-5, and c=-7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -5 to get 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+25-4%2A3%2A-7+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25-4%2A3%2A-7+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -5 to get 25  (note: remember when you square -5, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29%5E2=-5%2A-5=25 ALIGN=MIDDLE  ALT=\"%28-5%29%5E2=-5%2A-5=25\"   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+=+%285+%2B-+sqrt%28+25%2B84+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25%2B84+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-7%2A3 ALIGN=MIDDLE  ALT=\"-4%2A-7%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   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+=+%285+%2B-+sqrt%28+109+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+109+%29%29%2F%282%2A3%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+=+%285+%2B-+sqrt%28109%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28109%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6\r<BR>\n" );
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document.write( "Now 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+=+%285+%2B+sqrt%28109%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B+sqrt%28109%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+-+sqrt%28109%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%285+-+sqrt%28109%29%29%2F6\"   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=2.57338441815176 ALIGN=MIDDLE  ALT=\"x=2.57338441815176\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.906717751485092 ALIGN=MIDDLE  ALT=\"x=-0.906717751485092\"   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=2.5734 ALIGN=MIDDLE  ALT=\"x=2.5734\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.9067 ALIGN=MIDDLE  ALT=\"x=-0.9067\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So that means that the x-intercepts are \r<BR>\n" );
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document.write( "(-0.9067,0) and (2.5734,0)\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=3%2Ax%5E2-5%2Ax-7 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2-5%2Ax-7\"   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+-10.9067177514851%2C+12.5733844181518%2C+-10.9067177514851%2C+12.5733844181518%2C3%2Ax%5E2%2B-5%2Ax%2B-7%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=2.5734 ALIGN=MIDDLE  ALT=\"x=2.5734\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.9067 ALIGN=MIDDLE  ALT=\"x=-0.9067\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer<BR>\n" );
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