document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183951>Question 183951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2 + 14x+ 24 =0\r<BR>\n" );
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document.write( "ok so x^2 + 14x = -24\r<BR>\n" );
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document.write( "then my book says x^2 + 14x +49= 25  how did my text book get the 49?\r<BR>\n" );
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document.write( "then it continues (x + 7)^2 =25\r<BR>\n" );
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document.write( "x +7 = +-5\r<BR>\n" );
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document.write( "x=-7 +-5\r<BR>\n" );
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document.write( "so x= -2 or -12  i know how my book got the answer but not sure how my book got the 49 before(x+7)^2=25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138000 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=138000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 + 14x+ 24 =0<BR>\n" );
document.write( "Your book was solving it by completing the square like this:<BR>\n" );
document.write( "x^2+14x   =-24<BR>\n" );
document.write( "x^2+14x+49=-24+49 divide the 2nd term by 2 and square the result 49 and use it as the 3rd term and add 49 to the other side to keep everything equal.<BR>\n" );
document.write( "(x+7)^2=25<BR>\n" );
document.write( "x+7=+-5 sqrt of each side.<BR>\n" );
document.write( "x=-7+-5<BR>\n" );
document.write( "x=-12, x=-2<BR>\n" );
document.write( "You can also get the same answer by factoring or using the quadratic formula.<BR>\n" );
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document.write( "Ed<BR>\n" );
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document.write( "Factoring is easiest:<BR>\n" );
document.write( "(x+12)(x+2)=0<BR>\n" );
document.write( "x=-2, x=-12<BR>\n" );
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document.write( "Quadratic equation:<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%2B14x%2B24+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B24+=+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=%2814%29%5E2-4%2A1%2A24=100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2814%29%5E2-4%2A1%2A24=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=100 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+=+%28-14%2B-sqrt%28+100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-14%2B-sqrt%28+100+%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-%2814%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+-2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+-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-%2814%29-sqrt%28+100+%29%29%2F2%5C1+=+-12 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2814%29-sqrt%28+100+%29%29%2F2%5C1+=+-12\"   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%2B14x%2B24 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B24\"   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%2B14x%2B24+=+%28x--2%29%2A%28x--12%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B14x%2B24+=+%28x--2%29%2A%28x--12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2, -12.\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%2B14%2Ax%2B24+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B14%2Ax%2B24+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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