document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460074>Question 460074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following quadratic equations by factoring. <BR>\n" );
document.write( "x2 + x - 20 = 0 <BR>\n" );
document.write( "      	  x = 5<BR>\n" );
document.write( "      	  x = 4 <BR>\n" );
document.write( "      	  x = 4 or x = -5 <BR>\n" );
document.write( "      	  x = -4 or x = 5 \r<BR>\n" );
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document.write( "4. 2x2 – 15 = –7x <BR>\n" );
document.write( "      	  x = 1.5 or x = -3 <BR>\n" );
document.write( "      	  x = 1.5 or x = -5 <BR>\n" );
document.write( "      	  x = 3 or x = -5 <BR>\n" );
document.write( "      	  x = 1.5 or x = 5 \r<BR>\n" );
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document.write( "5. 3x2 – 5x = 2<BR>\n" );
document.write( "      	  x = 1/3 or x = 3 <BR>\n" );
document.write( "      	  x = 1/3 or x = 2 <BR>\n" );
document.write( "      	  x = -1/3 or x = 2 <BR>\n" );
document.write( "      	  x = - 1/3 or x = 3 \r<BR>\n" );
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document.write( "6. 3x2 + 3 = 10x <BR>\n" );
document.write( "      	  x = 1/3 or x = 3 <BR>\n" );
document.write( "      	  x = 1/3 or x = 2 <BR>\n" );
document.write( "      	  x = -1/3 or x = 2 <BR>\n" );
document.write( "      	  x = - 1/3 or x = 3 \r<BR>\n" );
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document.write( "7. Solve the following quadratic equations using the quadratic formula.\r<BR>\n" );
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document.write( "x2 + 7x + 9 = 0<BR>\n" );
document.write( "      	    <BR>\n" );
document.write( "      	    <BR>\n" );
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document.write( "      	    \r<BR>\n" );
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document.write( "8. x2 + 6x = 0 <BR>\n" );
document.write( "      	  x = 1 or x = 6 <BR>\n" );
document.write( "      	  x = 0 or x = 6 <BR>\n" );
document.write( "      	  x = 0 or x = -6 <BR>\n" );
document.write( "      	    \r<BR>\n" );
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document.write( "9. 15x2 – 7x – 2 = 0 <BR>\n" );
document.write( "      	  x = 2/3 or x = -1/5 <BR>\n" );
document.write( "      	  x = -2/3 or x = 1/5 <BR>\n" );
document.write( "      	  x = 3/2 or x = -5 <BR>\n" );
document.write( "      	  x = -3/2 or x = 5 \r<BR>\n" );
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document.write( "10. x2 - 9x + 5 = 0 <BR>\n" );
document.write( "      	    <BR>\n" );
document.write( "      	    <BR>\n" );
document.write( "      	    <BR>\n" );
document.write( "      	    <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315569 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9. 15x2 – 7x – 2 = 0 <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=15x%5E2%2B-7x%2B-2+=+0 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-7x%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" );
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=%28-7%29%5E2-4%2A15%2A-2=169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-7%29%5E2-4%2A15%2A-2=169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=169 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--7%2B-sqrt%28+169+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--7%2B-sqrt%28+169+%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-%28-7%29%2Bsqrt%28+169+%29%29%2F2%5C15+=+0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+169+%29%29%2F2%5C15+=+0.666666666666667\"   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-%28-7%29-sqrt%28+169+%29%29%2F2%5C15+=+-0.2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-7%29-sqrt%28+169+%29%29%2F2%5C15+=+-0.2\"   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=15x%5E2%2B-7x%2B-2 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-7x%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=15x%5E2%2B-7x%2B-2+=+%28x-0.666666666666667%29%2A%28x--0.2%29 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-7x%2B-2+=+%28x-0.666666666666667%29%2A%28x--0.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.666666666666667, -0.2.\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+15%2Ax%5E2%2B-7%2Ax%2B-2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-7%2Ax%2B-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the incorrect factoring by the solver.<BR>\n" );
document.write( "x = -1/5<BR>\n" );
document.write( "x = 2/3<BR>\n" );
document.write( "Do the others the same way.<BR>\n" );
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