document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90758>Question 90758</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh>Beginning Al</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square: 4x^2 + 2x - 3 = 0<BR>\n" );
document.write( "4x^2 + 2x = 3<BR>\n" );
document.write( "x^2 + 2/4x = 3/4<BR>\n" );
document.write( "Square one-half of the of the x-coefficient and then add it to both sides<BR>\n" );
document.write( "1/2 of 2/4 = 1/4^2 = 1/16<BR>\n" );
document.write( "x^2 + 2/4x + 1/16 = 3/4 + 1/16<BR>\n" );
document.write( "(x-1/4)^2 = 13/16<BR>\n" );
document.write( "x - 1/4 = +/- radical 13 over radical 16<BR>\n" );
document.write( "x - 1/4 = +/- radical 13 over 4<BR>\n" );
document.write( "x = 1/4 +/- radical 13 over 4<BR>\n" );
document.write( "x = 1 +/- radical 13 over 4 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66026 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=66026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A few minor errors in your work. The procedures you used were correct.<BR>\n" );
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document.write( "4x^2 + 2x - 3 = 0 <=== ok<BR>\n" );
document.write( "4x^2 + 2x = 3 <=== ok<BR>\n" );
document.write( "x^2 + 2/4x = 3/4 <=== good! <BR>\n" );
document.write( "Square one-half of the of the x-coefficient and then add it to both sides<BR>\n" );
document.write( "1/2 of 2/4 = 1/4^2 = 1/16 <=== ok<BR>\n" );
document.write( "x^2 + 2/4x + 1/16 = 3/4 + 1/16 <=== ok<BR>\n" );
document.write( "(x-1/4)^2 = 13/16 <=== minor error. In the parentheses the sign is + not - because the<BR>\n" );
document.write( "sign of the 2/4x term is + not minus.<BR>\n" );
document.write( "x - 1/4 = +/- radical 13 over radical 16 <=== left side should be x + 1/4<BR>\n" );
document.write( "x - 1/4 = +/- radical 13 over 4 <=== same. left side should be x + 1/4<BR>\n" );
document.write( "x = 1/4 +/- radical 13 over 4 <===the right side should be -1/4 +/- (radical 13)/4<BR>\n" );
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document.write( "This is the answer. If you want to write it as you did below you should use parentheses<BR>\n" );
document.write( "to indicate that both terms are divided by 4.<BR>\n" );
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document.write( "x = 1 +/- radical 13 over 4  should be x = (-1 +/- radical 13)/4<BR>\n" );
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document.write( "This will indicate that your answer is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-sqrt%2813%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-sqrt%2813%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The way you originally wrote it implies that only the radical 13 is divided by 4 and that<BR>\n" );
document.write( "the 1 is not.  It becomes much clearer what you meant if you put the entire quantity<BR>\n" );
document.write( "that is to be divided by 4 inside a set of parentheses.<BR>\n" );
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document.write( "The most critical thing about your method is that you show an understanding of what you<BR>\n" );
document.write( "are doing. A lot of students forget to divide to make the multiplier of the squared term<BR>\n" );
document.write( "become 1. Moving the constant to the right side early in the problem is not necessary<BR>\n" );
document.write( "but I like that you did it early in the problem. I always thought that it eliminated<BR>\n" );
document.write( "a lot of chances for error. And you correctly divided the multiplier of the x term by 2<BR>\n" );
document.write( "and squared it to find how much to add to each side of the equation.  Good job! The only<BR>\n" );
document.write( "check you need to make is when you write the squared term (in this problem it you wrote<BR>\n" );
document.write( "(x -1/4)^2, the constant term (1/4) should be the same as you get when you divide the<BR>\n" );
document.write( "multiplier of x (+2/4) by 2. In other words, when you divided the +2/4 by 2 you should have<BR>\n" );
document.write( "gotten +1/4 and that would be the term that appears inside the parentheses.<BR>\n" );
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document.write( "Hope this helps. Keep up the good work you are doing!!!<BR>\n" );
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