document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297684>Question 297684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}.  I cant understand how to solve the following problem using the quadratic formula:\r<BR>\n" );
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document.write( "z^2/1=z/5+6/5\r<BR>\n" );
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document.write( "I'm not sure if it's because it involves fractions and i just get really nervous but i'm not sure how to go about solving this problem... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214332 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This one can be factored too once you get it in the right form.<BR>\n" );
document.write( "z=-1 and 6/5<BR>\n" );
document.write( "First multiply through by 5<BR>\n" );
document.write( "5z^2=z+6<BR>\n" );
document.write( "5z^-z-6=0<BR>\n" );
document.write( "We need factors of -30 which add up to -1<BR>\n" );
document.write( "-6 and 5<BR>\n" );
document.write( "5z^2-6z+5z-6=0<BR>\n" );
document.write( "rearrange<BR>\n" );
document.write( "5z^2+5z-6z-6<BR>\n" );
document.write( "5z*(z+1)-6(z+1)=0<BR>\n" );
document.write( "(5z-6)*(z+1)=0<BR>\n" );
document.write( "Now the quadratic formula with the form 5z^2-x-6=0\r<BR>\n" );
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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=az%5E2%2Bbz%2Bc=0 ALIGN=MIDDLE  ALT=\"az%5E2%2Bbz%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5z%5E2%2B-1z%2B-6+=+0 ALIGN=MIDDLE  ALT=\"5z%5E2%2B-1z%2B-6+=+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=z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"z%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=%28-1%29%5E2-4%2A5%2A-6=121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1%29%5E2-4%2A5%2A-6=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=121 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--1%2B-sqrt%28+121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1%2B-sqrt%28+121+%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=z%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C5+=+1.2 ALIGN=MIDDLE  ALT=\"z%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C5+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C5+=+-1 ALIGN=MIDDLE  ALT=\"z%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C5+=+-1\"   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=5z%5E2%2B-1z%2B-6 ALIGN=MIDDLE  ALT=\"5z%5E2%2B-1z%2B-6\"   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=5z%5E2%2B-1z%2B-6+=+5%28z-1.2%29%2A%28z--1%29 ALIGN=MIDDLE  ALT=\"5z%5E2%2B-1z%2B-6+=+5%28z-1.2%29%2A%28z--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.2, -1.\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+5%2Ax%5E2%2B-1%2Ax%2B-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-1%2Ax%2B-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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