document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515573>Question 515573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble trying to solve this problem.  Would someobdy be able to assist me?\r<BR>\n" );
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document.write( "Solve - 3x^2 - 7x - 5 = 0<BR>\n" );
document.write( "a.  The solutions(s) is/are x=?<BR>\n" );
document.write( "b.  Find the x-intercepts of f(x) = 3x^2 -7x - 5.\r<BR>\n" );
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document.write( "1/3 x 3x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3 = 0<BR>\n" );
document.write( "x^2 - 7/3x - 5/3  this is where I get lost.\r<BR>\n" );
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document.write( "Thank you.\r<BR>\n" );
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document.write( "Sincerely,\r<BR>\n" );
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document.write( "Christine Fitzgerald </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344072 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><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=344072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given the quadratic equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2+-+7x+-+5+=+0 ALIGN=MIDDLE  ALT=\"-3x%5E2+-+7x+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It looks like you are trying to factor this quadratic, but the easiest way to solve this one is to use the quadratic formula: recall that the solutions to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "are\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( "Here, a = -3, b = -7, and c = -5, so we substitute in and get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A%28-3%29%2A%28-5%29+%29%29%2F%282%2A%28-3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287+%2B-+sqrt%28+49+-+60+%29%29%2F%28-6%29+ ALIGN=MIDDLE  ALT=\"x+=+%287+%2B-+sqrt%28+49+-+60+%29%29%2F%28-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simplifying)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287+%2B-+sqrt%28-11%29%29%2F%28-6%29+ ALIGN=MIDDLE  ALT=\"x+=+%287+%2B-+sqrt%28-11%29%29%2F%28-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simplifying)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%287+%2B-+i%2A+sqrt%2811%29%29%2F%28-6%29+ ALIGN=MIDDLE  ALT=\"+x+=+%287+%2B-+i%2A+sqrt%2811%29%29%2F%28-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-11%29+=+sqrt%28-1%29%2Asqrt%2811%29+=+i%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%28-11%29+=+sqrt%28-1%29%2Asqrt%2811%29+=+i%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "So the two solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287+%2B+i+%2A+sqrt%2811%29%29%2F%28-6%29+=+%28-7+-+i+%2A+sqrt%2811%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%287+%2B+i+%2A+sqrt%2811%29%29%2F%28-6%29+=+%28-7+-+i+%2A+sqrt%2811%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%287+-+i+%2A+sqrt%2811%29%29%2F%28-6%29+=+%28-7+%2B+i+%2A+sqrt%2811%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%287+-+i+%2A+sqrt%2811%29%29%2F%28-6%29+=+%28-7+%2B+i+%2A+sqrt%2811%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, the x-intercepts of the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the REAL roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2Bc+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If the quadratic equation has no real roots, then the graph never intersects the x-axis: it is either always above the x-axis, or always below it.  In this case, the solution to the quadratic equation are non-real complex numbers, so there are no x-intercepts of f(x). </SPAN>\n" );
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