document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281364>Question 281364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a quadratic equation having the given numbers as solutions. -3.5, 2.2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204377 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=204377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of a quadratic equation that has been solved is to have two factors that are multiplied.  In this case, you're told the solutions are x= -3.5 and x=2.2.  So the factored form of the equation would be:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x + 3.5)(x - 2.2) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using FOIL...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x^2 -2.2x +3.5x -7.7 = 0<BR>\n" );
document.write( "x^2 + 1.3x - 7.7 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "multiply by 10 to get rid of the decimals...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "10x^2 + 13x - 77 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking this equation using the quadratic formula, you can determine if the solutions are x= -3.5 and x= 2.2...<BR>\n" );
document.write( ".<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=10x%5E2%2B13x%2B-77+=+0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B13x%2B-77+=+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=%2813%29%5E2-4%2A10%2A-77=3249 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A10%2A-77=3249\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3249 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+=+%28-13%2B-sqrt%28+3249+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+3249+%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-%2813%29%2Bsqrt%28+3249+%29%29%2F2%5C10+=+2.2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+3249+%29%29%2F2%5C10+=+2.2\"   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-%2813%29-sqrt%28+3249+%29%29%2F2%5C10+=+-3.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2813%29-sqrt%28+3249+%29%29%2F2%5C10+=+-3.5\"   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=10x%5E2%2B13x%2B-77 ALIGN=MIDDLE  ALT=\"10x%5E2%2B13x%2B-77\"   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=10x%5E2%2B13x%2B-77+=+10%28x-2.2%29%2A%28x--3.5%29 ALIGN=MIDDLE  ALT=\"10x%5E2%2B13x%2B-77+=+10%28x-2.2%29%2A%28x--3.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.2, -3.5.\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+10%2Ax%5E2%2B13%2Ax%2B-77+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B13%2Ax%2B-77+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "Done </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );