document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141122>Question 141122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For 5x^2+3x-2  do the following \r<BR>\n" );
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document.write( "-graphing (both in vertex form and in standard form)<BR>\n" );
document.write( "-factoring/pp <BR>\n" );
document.write( "-completing the square/square roots<BR>\n" );
document.write( "-quadratic formula. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102798 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x^2+3x-2=0<BR>\n" );
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document.write( "factoring:<BR>\n" );
document.write( "5*-2=-10<BR>\n" );
document.write( "What 2 factors of -10 add up 3? Ans: 5 and -2.<BR>\n" );
document.write( "5x^2+5x-2x-2=0<BR>\n" );
document.write( "5x(x+1)-2(x+1)=0 Factoring by grouping.<BR>\n" );
document.write( "(5x-2)(x+1)=0<BR>\n" );
document.write( "5x=2 x=2/5<BR>\n" );
document.write( "x=-1<BR>\n" );
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document.write( "Completing the square:<BR>\n" );
document.write( "5x^2+3x-2=0<BR>\n" );
document.write( "x^2+ 3x/5 - 2/5 = 0<BR>\n" );
document.write( "x^2+.6x-.4=0<BR>\n" );
document.write( "x^2+.6x =.4<BR>\n" );
document.write( "x^2+.6x+.09=.4+.09 Complete the square by dividing the middle term by 2 and squaring the result.<BR>\n" );
document.write( "(x+.3)^2=.49<BR>\n" );
document.write( "x+.3=+-.7<BR>\n" );
document.write( "x=-.3+-.7<BR>\n" );
document.write( "x=.4, x=-1<BR>\n" );
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document.write( "Ed<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=5x%5E2%2B3x%2B-2+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B3x%2B-2+=+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" );
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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" );
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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=%283%29%5E2-4%2A5%2A-2=49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A5%2A-2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=49 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+=+%28-3%2B-sqrt%28+49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+49+%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-%283%29%2Bsqrt%28+49+%29%29%2F2%5C5+=+0.4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+49+%29%29%2F2%5C5+=+0.4\"   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-%283%29-sqrt%28+49+%29%29%2F2%5C5+=+-1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%283%29-sqrt%28+49+%29%29%2F2%5C5+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B3x%2B-2 ALIGN=MIDDLE  ALT=\"5x%5E2%2B3x%2B-2\"   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=5x%5E2%2B3x%2B-2+=+%28x-0.4%29%2A%28x--1%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B3x%2B-2+=+%28x-0.4%29%2A%28x--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.4, -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%2B3%2Ax%2B-2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B3%2Ax%2B-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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