document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188260>Question 188260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by Factorization\r<BR>\n" );
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document.write( "1. x2 - 13x + 30 = 0 \r<BR>\n" );
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document.write( "2. 2x2 - 3x = 2\r<BR>\n" );
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document.write( "3. 3x2 - 7x - 6 = 0 \r<BR>\n" );
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document.write( "4. 5x2 - 40 x = 0\r<BR>\n" );
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document.write( "5. 36x2 - 81 = 0 \r<BR>\n" );
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document.write( "6. 4x2 - 16 = 0 \r<BR>\n" );
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document.write( "7. 3x2 = 4x + 7\r<BR>\n" );
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document.write( "8. x2 + 2x = 0\r<BR>\n" );
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document.write( "9. 5x2 - 40 x = 0 \r<BR>\n" );
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document.write( "10. x2 + x = 0 \r<BR>\n" );
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document.write( "Solve By Quadratic Formula\r<BR>\n" );
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document.write( "1. 2x2 - 6x + 3 = 0 \r<BR>\n" );
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document.write( "2. 7x2 + 4x = 1\r<BR>\n" );
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document.write( "3. 2x2 + 6x + 3 = 0 \r<BR>\n" );
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document.write( "4. x2 - 5x + 6 = 0 \r<BR>\n" );
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document.write( "5. 3x2 = 4x + 5<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 #141128 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=141128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by Factorization <BR>\n" );
document.write( "1. x2 - 13x + 30 = 0 <BR>\n" );
document.write( "This one is easy, you do it.<BR>\n" );
document.write( "2. 2x2 - 3x = 2<BR>\n" );
document.write( "2x^2 - 3x - 2 = 0<BR>\n" );
document.write( "(2x + 1)*(x - 2) - 0<BR>\n" );
document.write( "x = 2, x = -1/2<BR>\n" );
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document.write( "3. 3x2 - 7x - 6 = 0 <BR>\n" );
document.write( "4. 5x2 - 40 x = 0 <BR>\n" );
document.write( "5. 36x2 - 81 = 0 Divide by 9<BR>\n" );
document.write( "x^2 - 9 = 0<BR>\n" );
document.write( "A difference of 2 squares is ALWAYS the product of the sum and difference of the roots.<BR>\n" );
document.write( "sum = x + 3<BR>\n" );
document.write( "difference = x - 3<BR>\n" );
document.write( "(x+3)*(x-3)= 0<BR>\n" );
document.write( "x = +3, x = -3<BR>\n" );
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document.write( "6. 4x2 - 16 = 0 Divide by 4<BR>\n" );
document.write( "7. 3x2 = 4x + 7 <BR>\n" );
document.write( "8. x2 + 2x = 0 <BR>\n" );
document.write( "9. 5x2 - 40 x = 0 <BR>\n" );
document.write( "10. x2 + x = 0 <BR>\n" );
document.write( "Solve By Quadratic Formula <BR>\n" );
document.write( "1. 2x2 - 6x + 3 = 0 <BR>\n" );
document.write( "2. 7x2 + 4x = 1 <BR>\n" );
document.write( "3. 2x2 + 6x + 3 = 0 <BR>\n" );
document.write( "4. x2 - 5x + 6 = 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=1x%5E2%2B-5x%2B6+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6+=+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" );
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=%28-5%29%5E2-4%2A1%2A6=1 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A1%2A6=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1 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--5%2B-sqrt%28+1+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+1+%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-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+3\"   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-%28-5%29-sqrt%28+1+%29%29%2F2%5C1+=+2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5%29-sqrt%28+1+%29%29%2F2%5C1+=+2\"   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=1x%5E2%2B-5x%2B6 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6\"   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%2B-5x%2B6+=+%28x-3%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-5x%2B6+=+%28x-3%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, 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+1%2Ax%5E2%2B-5%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "5. 3x2 = 4x + 5<BR>\n" );
document.write( "You can email me via the thank you note for assistance, or to check your work.<BR>\n" );
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