document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761441>Question 761441</A>: <I><SPAN STYLE=\"word-break: break-all;\"> whats the answer for x^2+4x+10=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463223 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=463223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+4X+%2B+10+=+3 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+4X+%2B+10+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set the equation to 0 by subtracting 3 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+4X+%2B+10+-+3+=+3+-+3 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+4X+%2B+10+-+3+=+3+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2+%2B+4X+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"X%5E2+%2B+4X+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can now use the quadratic equation.<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=1X%5E2%2B4X%2B7+=+0 ALIGN=MIDDLE  ALT=\"1X%5E2%2B4X%2B7+=+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=%284%29%5E2-4%2A1%2A7=-12 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A1%2A7=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -12 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -12 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+12%29+=+3.46410161513775 ALIGN=MIDDLE  ALT=\"sqrt%28+12%29+=+3.46410161513775\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5B12%5D+=+%28-4%2B-+i%2Asqrt%28+-12+%29%29%2F2%5C1+=++%28-4%2B-+i%2A3.46410161513775%29%2F2%5C1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\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%2B4%2Ax%2B7+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B7+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Since the discriminant is less than 0, there are no solutions without using imaginary numbers. This is why the graph never touches the X-axis. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );