document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113094>Question 113094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x^= 13x + 12\r<BR>\n" );
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document.write( "Am I right by stating that there is no solution to this problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82357 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I presume you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2=13x%2B12 ALIGN=MIDDLE  ALT=\"4x%5E2=13x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I'm not certain why you are saying there is no solution.  In fact there is always a solution to a quadratic, in fact there are always two solutions.  They aren't always to be found in the real number system, but there are always two answers.\r<BR>\n" );
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document.write( "I suspect that you tried to use the quadratic formula:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, without putting the equation in standard form.  That would result in a negative radicand (the part under the radical) and that may have led you to believe that there is no solution.  (That, in itself, is an erroneous belief.  The only thing is that when you have a negative radicand, the solution is no longer a pair of real numbers, it becomes a pair of complex numbers -- but that is a tale for another time)\r<BR>\n" );
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document.write( "Remember, the quadratic formula is the solution to <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;\" >, so in order to process your equation, you needed to put it in that form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2=+13x+%2B+12 ALIGN=MIDDLE  ALT=\"4x%5E2=+13x+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-13x-12=0 ALIGN=MIDDLE  ALT=\"4x%5E2-13x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can see that a = 4, b = -13, and c = -12.  Putting those values into the quadratic formula yields:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A4%2A%28-12%29+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A4%2A%28-12%29+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2813+%2B-+sqrt%28+169%2B192+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2813+%2B-+sqrt%28+169%2B192+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2813+%2B-+sqrt%28+361+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2813+%2B-+sqrt%28+361+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28361%29=19 ALIGN=MIDDLE  ALT=\"sqrt%28361%29=19\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2813-19%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2813-19%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2813%2B19%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2813%2B19%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now that I have done this with the quadratic formula and discovered that the solution set contains two rational numbers, I know that the trinomial could have been factored.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-13x-12=%284x%2B3%29%28x-4%29 ALIGN=MIDDLE  ALT=\"4x%5E2-13x-12=%284x%2B3%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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