document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285345>Question 285345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> im a little confused as to what to do with the exponent in this situation. My teacher taught us in class but now that im home my mind went blank. The answer i came up with is -1. But the answers that were provided on this site are -2 and -4. Here is the problem: x^2 + 6x + 8 = 0 Here's what i did: x*x+6x+8=0 2x+6x+8=0 8x+8=0 8x=-8 x=-1...Someone just sent me an answer that just said factor (x+4)(x+2)=0....I'm even more confused now...IS THERE ANYONE THAT CAN BREAK THIS PROBLEM DOWN FOR ME STEP BY STEP PLEASE...THANK YOU!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206873 by </B><A HREF=/tutors/aboutme.mpl?userid=Deina><B>Deina(147)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Deina><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/cgi-bin/show-face.mpl?user=Deina><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=206873\">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=+x%5E2+%2B+6x+%2B+8+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+6x+%2B+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <b>quadratic equation</b>, so use the <BR>\n" );
document.write( "formula <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;\" > <br><BR>\n" );
document.write( "in this case we have:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = 8\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%2C2%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2a+ ALIGN=MIDDLE  ALT=\"+x%5B1%2C2%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that you will have <b>two answers!</b><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B6x%2B8+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%286%29%5E2-4%2A1%2A8=4 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%286%29%5E2-4%2A1%2A8=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-6%2B-sqrt%28+4+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-6%2B-sqrt%28+4+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%286%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+-2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%286%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%286%29-sqrt%28+4+%29%29%2F2%5C1+=+-4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%286%29-sqrt%28+4+%29%29%2F2%5C1+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B6x%2B8 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B6x%2B8+=+1%28x--2%29%2A%28x--4%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B6x%2B8+=+1%28x--2%29%2A%28x--4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2, -4.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( "<br><BR>\n" );
document.write( "Quadratics have always been one of my favorite equations, because they are <i>so much easier</i> than factoring!\r<BR>\n" );
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document.write( "Go through the quadratic explanation above several times. Once you think you understand it, use some different numbers and see if you can calculate it out to the same answer the computer gives you until you're sure that you understand it. It will save you <b>massive</b> amounts of work in the future! \r<BR>\n" );
document.write( "\n" );
document.write( "Once you understand the quadratic, bob's your uncle!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );