document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167340>Question 167340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble understanding and solving quadratic equations.  x^2-2x-13=0<BR>\n" );
document.write( "and 4x^2-4x+3=0<BR>\n" );
document.write( "The steps I need to use are:<BR>\n" );
document.write( "a.  move the constant term to the right side of the equation<BR>\n" );
document.write( "b.  multiply each term in the equation by four times the coefficient of the x^2 term.<BR>\n" );
document.write( "c.   square the coefficient of the original  x term and add it to both sides of the equation<BR>\n" );
document.write( "d.  Take the square root from both sides<BR>\n" );
document.write( "e.  Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.<BR>\n" );
document.write( "f.  set the left side of the equation equal to the negative square root of the numberon the right side of the equation and solve for x\r<BR>\n" );
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document.write( "I have to solve these kind of questions on a test and I am lost.  This is what I have so far:  x^2-2x-13=0<BR>\n" );
document.write( "                x^2 -2x=13<BR>\n" );
document.write( "                4x^2-8x=52<BR>\n" );
document.write( "Can you help me?<BR>\n" );
document.write( "~Jenn<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 #123238 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your method is called \"completing the square\"...<BR>\n" );
document.write( "This site explains it quite nicely:<BR>\n" );
document.write( "http://www.purplemath.com/modules/sqrquad.htm<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x^2-2x-13=0<BR>\n" );
document.write( "x^2-2x = 13<BR>\n" );
document.write( "Take half the 'b' coefficient and square it:[(1/2)(-2)]^2 = [-1]^1 = 1 <BR>\n" );
document.write( "x^2-2x+1 = 13+1  (since you added 1 to left, do so on the right - for balance)<BR>\n" );
document.write( "(x-1)^2 = 14<BR>\n" );
document.write( "x-1 = sqrt(14)<BR>\n" );
document.write( "x = 1(+-)sqrt(14)<BR>\n" );
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document.write( "That's 1 \"plus or minus\" square root of 14.<BR>\n" );
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document.write( "4x^2-4x+3=0<BR>\n" );
document.write( "4x^2-4x = -3<BR>\n" );
document.write( "factor the 4 on the left:<BR>\n" );
document.write( "4(x^2-x) = -3<BR>\n" );
document.write( "(x^2-x) = -3/4<BR>\n" );
document.write( "(x^2-x+(1/4)) = -3/4 + 1/4<BR>\n" );
document.write( "(x-(1/2))^2 = -2/4<BR>\n" );
document.write( "x-(1/2) = sqrt(-2/4)<BR>\n" );
document.write( "x = (1/2)(+-)sqrt(-1/2)<BR>\n" );
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document.write( "Since the term inside the sqrt is negative -- we have no real solutions -- rather, we have two imaginary solutions.<BR>\n" );
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document.write( "You could see the same thing using the \"quadratic equation\" below:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B-4x%2B3+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-4x%2B3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-4%29%5E2-4%2A4%2A3=-32 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4%29%5E2-4%2A4%2A3=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -32 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -32 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+32%29+=+5.65685424949238 ALIGN=MIDDLE  ALT=\"sqrt%28+32%29+=+5.65685424949238\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--4%2B-+i%2Asqrt%28+-32+%29%29%2F2%5C4+=++%28--4%2B-+i%2A5.65685424949238%29%2F2%5C4+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B3+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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