document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248228>Question 248228</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Solve by applying the Quadratic Formula. Show your work.thanks\r<BR>\n" );
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document.write( "p^2 + 3p - 9 = 0  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180906 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=180906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p^2 + 3p - 9 = 0<BR>\n" );
document.write( "what is the quadratic formula?<BR>\n" );
document.write( "the quadratic equation is ax^2+bx+c=0<BR>\n" );
document.write( "in your equation a=1; b=3 and c=-9<BR>\n" );
document.write( "we solve for x to get the quadratic formula<BR>\n" );
document.write( "It is wise to calculate the discriminant (b^2-4ac) first. You have to do it anyways.<BR>\n" );
document.write( "It will tell you about the solutions.<BR>\n" );
document.write( "It says that your equation can be factored but that is not normal factoring\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=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%2B3x%2B-9+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-9+=+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=%283%29%5E2-4%2A1%2A-9=45 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A-9=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=45 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+45+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+45+%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+45+%29%29%2F2%5C1+=+1.85410196624968 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+45+%29%29%2F2%5C1+=+1.85410196624968\"   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+45+%29%29%2F2%5C1+=+-4.85410196624968 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%283%29-sqrt%28+45+%29%29%2F2%5C1+=+-4.85410196624968\"   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=1x%5E2%2B3x%2B-9 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-9\"   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%2B3x%2B-9+=+1%28x-1.85410196624968%29%2A%28x--4.85410196624968%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B-9+=+1%28x-1.85410196624968%29%2A%28x--4.85410196624968%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.85410196624968, -4.85410196624968.\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%2B3%2Ax%2B-9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " What other way can we solve this equation?<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "p^2 + 3p - 9 = 0<BR>\n" );
document.write( "p^2+3p=9=36/4<BR>\n" );
document.write( "add (3/2)^2 to both sides<BR>\n" );
document.write( "p^2+3p+9/4=(36+9)/4<BR>\n" );
document.write( "p^2+3p+9/4=(45)/4<BR>\n" );
document.write( "factor <BR>\n" );
document.write( "(p+3/2)^2=(3sqrt(5)/2)^2<BR>\n" );
document.write( "p+3/2=+\-(3sqrt)5//2<BR>\n" );
document.write( "subtract 3/2 from both sides<BR>\n" );
document.write( "p=-3/2+3sqrt(5)/2<BR>\n" );
document.write( "p=-3/2-3sqrt(5)/2<BR>\n" );
document.write( "factor out 3/2 </SPAN>\n" );
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