document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116773>Question 116773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by using the quadratic formula: 3x^2+4x-15=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84896 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=84896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B4x-15=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B4x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is in the standard quadratic form of:<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( "By comparing the standard form to the given problem, you can see that a = 3, b = 4, and c = -15<BR>\n" );
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document.write( "For the standard form, the values of x that satisfy the equation are given by:<BR>\n" );
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document.write( "<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;\" ><BR>\n" );
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document.write( "So all you have to do to solve the given equation is to substitute 3 for a, 4 for b, and -15<BR>\n" );
document.write( "for c into the equation for x. When you do, that equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%284%29+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-15%29+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-15%29+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the denominator 2*3 = 6 to make the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%284%29+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-15%29+%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-15%29+%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Work inside the radical. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2+=+16 ALIGN=MIDDLE  ALT=\"4%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A3%2A%28-15%29+=+180 ALIGN=MIDDLE  ALT=\"-4%2A3%2A%28-15%29+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substituting <BR>\n" );
document.write( "these values results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%284%29+%2B-+sqrt%28+16%2B180%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28+16%2B180%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the terms in the radical:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%284%29+%2B-+sqrt%28+196%29%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28+196%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But the square root of 196 is 14. Substituting this results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%284%29+%2B-+14%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+14%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that -(4) = -4 which simplifies the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+14%29%2F6+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+14%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So there are two possible values of x as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+14%29%2F6++=+10%2F6+=+5%2F3 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+14%29%2F6++=+10%2F6+=+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+14%29%2F6+=+-18%2F6+=+-3 ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+14%29%2F6+=+-18%2F6+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Those are the two answers. Hope this helps to familiarize you with the quadratic equation and<BR>\n" );
document.write( "how it can be used to solve quadratic equations. <BR>\n" );
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