document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100472>Question 100472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello:\r<BR>\n" );
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document.write( "Thank you so much for offering the free tutoring.\r<BR>\n" );
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document.write( "My exercise is:\r<BR>\n" );
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document.write( "x^2+4x+4=7.\r<BR>\n" );
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document.write( "I have gotten to:\r<BR>\n" );
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document.write( "x^2+4x+4=7=0<BR>\n" );
document.write( "x^2+4x+(-3)=0<BR>\n" );
document.write( "now I am stuck.\r<BR>\n" );
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document.write( "Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73176 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=73176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The most common ways to solve a quadratic equation are by graphing, factoring, and completing<BR>\n" );
document.write( "the square.  Graphing has the disadvantage of being slow and requiring the scale to be<BR>\n" );
document.write( "big enough so you can read it accurately. Factoring into a \"nice\" set of factors is not <BR>\n" );
document.write( "always possible. (That is the case with this problem.) But completing the square can be<BR>\n" );
document.write( "counted on to give you an answer.  Using the quadratic formula is just a convenient <BR>\n" );
document.write( "form of completing the square.<BR>\n" );
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document.write( "The quadratic formula says that if you can arrange the quadratic equation into the standard 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 solutions will be 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+=+%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( "You have worked your problem down to the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B%28-3%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B%28-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's just remove the parentheses on the left side to make the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that this compares to the standard form in which a = +1, b = +4, and c = -3.<BR>\n" );
document.write( "Therefore, you can go to the solutions equation and substitute these values of a, b, and c<BR>\n" );
document.write( "into it to get the answers for x.<BR>\n" );
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document.write( "Start with the solutions equation:<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( "and substitute +1 for a, +4 for b, and -3 for c to get:<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+%284%29%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "within the radical sign note that <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%2A1%2A%28-3%29+=+12 ALIGN=MIDDLE  ALT=\"-4%2A1%2A%28-3%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting<BR>\n" );
document.write( "these into the radical 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-%284%29+%2B-+sqrt%28++16%2B12%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%28++16%2B12%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the terms in the radical combine to 28 to give:<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%2828%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+sqrt%2828%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the radical can be simplified. By the rules of radicals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29+=+2%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29+=+2%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2828%29 ALIGN=MIDDLE  ALT=\"sqrt%2828%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be replaced by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer equation <BR>\n" );
document.write( "simplifies to:<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-+2%2Asqrt%287%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%284%29+%2B-+2%2Asqrt%287%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now, remove the parentheses from -(4) to make it just -1 and multiply the 2*1 in the denominator<BR>\n" );
document.write( "to get just 2. With these changes the answer equation simplifies 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-+2%2Asqrt%287%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the two answers to your problem are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+2%2Asqrt%287%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+2%2Asqrt%287%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+2%2Asqrt%287%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+2%2Asqrt%287%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can approximate these answers by using a calculator to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29+=+2.645751311 ALIGN=MIDDLE  ALT=\"sqrt%287%29+=+2.645751311\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substituting that into the two answers results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+2%2A2.645751311%29%2F2+=+%28-4+%2B+5.291502622%29%2F2+=+1.291502622%2F2+=+0.645751311 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "for one answer and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+2%2A2.645751311%29%2F2+=+%28-4+-+5.291502622%29%2F2+=+-9.291502622%2F2+=+-4.645751311 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "for the other answer.<BR>\n" );
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document.write( "In summary, the two answers are x = 0.645751311 and x = -4.645751311<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better and gets you familiar with<BR>\n" );
document.write( "using the quadratic formula as a method you can count on to solve a quadratic equation <BR>\n" );
document.write( "that is giving you trouble.<BR>\n" );
document.write( " </SPAN>\n" );
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