document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71395>Question 71395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve: 3x(to the 2nd power) - 2x - 4 = 0\r<BR>\n" );
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document.write( "Please show work and solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51070 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+2x+-+4+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-+2x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation does not factor nicely. So the best way to solve it is to use the quadratic <BR>\n" );
document.write( "formula. (The quadratic formula is derived by the method of completing the square, <BR>\n" );
document.write( "so it is a generalized form of the process of completing the square.)<BR>\n" );
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document.write( "The quadratic formula says that for an expression of the quadratic form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The value(s) of x is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28b%29%2F2a+%2B-+%28sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+-%28b%29%2F2a+%2B-+%28sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By comparing the numeric values given in the problem with the letters in the quadratic <BR>\n" );
document.write( "form you can see that a (the coefficient of x^2) is 3, b (the coefficient of x is -2, <BR>\n" );
document.write( "and c (the constant) is -4.  Now all you have to do is substitute those values into the <BR>\n" );
document.write( "equation for x.  When you do you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28-2%29%2F%282%2A3%29+%2B-+%28sqrt%28%28-2%29%5E2+-+4%2A3%2A%28-4%29%29%29%2F%282%2A3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first stage of simplification results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F6+%2B-+%28sqrt%284+%2B+48%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+2%2F6+%2B-+%28sqrt%284+%2B+48%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the square root term becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2852%29 ALIGN=MIDDLE  ALT=\"sqrt%2852%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%2A4%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "which furthermore can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29+%2A+sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29+%2A+sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But the square root of <BR>\n" );
document.write( "4 is 2, so the final reduction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2813%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Put this into the equation as a <BR>\n" );
document.write( "replacement for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2B48%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2B48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F6+%2B-+%282%2Asqrt%2813%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+2%2F6+%2B-+%282%2Asqrt%2813%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The six is a common denominator so you can put both numerators over this common denominator <BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+%282%2Asqrt%2813%29%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+%282%2Asqrt%2813%29%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And since 2 is a factor of both terms in the numerator it can be made a multiplier <BR>\n" );
document.write( "of the two numerator terms as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282%2A%281+%2B-+sqrt%2813%29%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%282%2A%281+%2B-+sqrt%2813%29%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, the multiplier of two in the numerator and the denominator have a common <BR>\n" );
document.write( "factor of 2.  Cancel it to make the final answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%281+%2B-+sqrt%2813%29%29%29%2F3 ALIGN=MIDDLE  ALT=\"x+=+%28%281+%2B-+sqrt%2813%29%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "These are the two values for x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%281+%2B+sqrt%2813%29%29%29%2F3 ALIGN=MIDDLE  ALT=\"x+=+%28%281+%2B+sqrt%2813%29%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%281+-+sqrt%2813%29%29%29%2F3 ALIGN=MIDDLE  ALT=\"x+=+%28%281+-+sqrt%2813%29%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to see how to work this equation.  Make sure that you work through <BR>\n" );
document.write( "each step so you can see how to identify a, b, and c in a quadratic equation, and then <BR>\n" );
document.write( "how to work the numbers. This method is useful because it is a general method that can <BR>\n" );
document.write( "be used to evaluate and solve quadratic equations, some significantly more complex <BR>\n" );
document.write( "than this one. </SPAN>\n" );
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