document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177853>Question 177853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square. Show your work.[please]\r<BR>\n" );
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document.write( "29. 2x2 - 6x + 1 = 0\r<BR>\n" );
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document.write( " 30. -x2 - 8x + 5 = 0\r<BR>\n" );
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document.write( "31. 9x2 - 18x - 1 = 0\r<BR>\n" );
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document.write( " 32. -4x2 + 8x - 3 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132891 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=132891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation # 29 is: ******************************************************<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+-+6%2Ax+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+-+6%2Ax+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "standard form of the equation is:<BR>\n" );
document.write( "ax^2 + bx + c = 0<BR>\n" );
document.write( "this is already in standard form.<BR>\n" );
document.write( "a term = 2<BR>\n" );
document.write( "b term = (-6)<BR>\n" );
document.write( "c term = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "first you move the constant to the right side of the equation by subtracting 1 from both sides of the equation to get :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+-+6%2Ax+=+-1 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+-+6%2Ax+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then divide both sides of the equation by 2 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3%2Ax+=+%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+3%2Ax+=+%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take half of 3 and factor the left side of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+%283%2F2%29%29%5E2+-+%283%2F2%29%5E2+=+%28-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28x+-+%283%2F2%29%29%5E2+-+%283%2F2%29%5E2+=+%28-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this takes a little explaining.<BR>\n" );
document.write( "start of explanation.<BR>\n" );
document.write( "here's an example (not anything to do with this problem because the numbers are changed to make it simple).<BR>\n" );
document.write( "take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "if you take half the 2 and make this equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the answer will be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+%2B+%281%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+%2B+%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2 ALIGN=MIDDLE  ALT=\"%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is extra, so you have to subtract it to keep the original equality intact.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2+-+1+=+%28x%5E2+%2B+2x+%2B+1%29-+1+=+x%5E2+%2B+2x ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2+-+1+=+%28x%5E2+%2B+2x+%2B+1%29-+1+=+x%5E2+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is what you started off with.<BR>\n" );
document.write( "this is exactly what we did above:<BR>\n" );
document.write( "we took <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3%2Ax ALIGN=MIDDLE  ALT=\"x%5E2+-+3%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > and factored it to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2+-+%283%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2+-+%283%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if you do the multiplication, you will see that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2+-+%283%2F2%29%5E2+=+x%5E2+-+3x+%2B+%283%2F2%29%5E2+-+%283%2F2%29%5E2+=+x%5E2+-+3x ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "end of explanation.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then add the (3/2)^2 term to both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+%283%2F2%29%29%5E2+=+%28-%281%2F2%29%29+%2B+%283%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+%283%2F2%29%29%5E2+=+%28-%281%2F2%29%29+%2B+%283%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take the square root of both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+%283%2F2%29 ALIGN=MIDDLE  ALT=\"x+-+%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-1%2F2%29+%2B+%283%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-1%2F2%29+%2B+%283%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then add ((3/2)) to both sides of the equation to get:<BR>\n" );
document.write( "x = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28%28-1%2F2%29+%2B+%283%2F2%29%5E2%29%29+%2B+%283%2F2%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28%28-1%2F2%29+%2B+%283%2F2%29%5E2%29%29+%2B+%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "after doing the math (i used a calculator), you will get:<BR>\n" );
document.write( "x = 2.8228...<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = .1771...<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)<BR>\n" );
document.write( "i took the original equation of 2x^2 - 6x + 1 = 0<BR>\n" );
document.write( "and substituted these values to get:<BR>\n" );
document.write( "0 = 0 both times proving both values are good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "equation number 32 is: ***********************************************<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Ax%5E2+%2B+8%2Ax+-+3+=+0 ALIGN=MIDDLE  ALT=\"-4%2Ax%5E2+%2B+8%2Ax+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "standard form of the equation is:<BR>\n" );
document.write( "ax^2 + bx + c = 0<BR>\n" );
document.write( "this is already in standard form.<BR>\n" );
document.write( "a term = -4<BR>\n" );
document.write( "b term = 8<BR>\n" );
document.write( "c term = -3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "first you move the constant to the right side of the equation by adding 3 to both sides of the equation to get :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Ax%5E2+%2B+8%2Ax+=+3 ALIGN=MIDDLE  ALT=\"-4%2Ax%5E2+%2B+8%2Ax+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then divide both sides of the equation by (-4) to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2%2Ax+=+-3%2F4 ALIGN=MIDDLE  ALT=\"x%5E2+-+2%2Ax+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take half of 2 and factor the left side of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29%5E2+-+%281%29%5E2+=+-3%2F4%29 ALIGN=MIDDLE  ALT=\"%28x+-+1%29%5E2+-+%281%29%5E2+=+-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then add the (1)^2 term to both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+=+%28-3%2F4%29+%2B+1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+=+%28-3%2F4%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take the square root of both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-3%2F4%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-3%2F4%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then add 1 to both sides of the equation to get:<BR>\n" );
document.write( "x = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28%28-3%2F4%29+%2B+1%29%29+%2B+1 ALIGN=MIDDLE  ALT=\"%28sqrt%28%28-3%2F4%29+%2B+1%29%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "after doing the math (i used a calculator), you will get:<BR>\n" );
document.write( "x = 1.5<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = .5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)<BR>\n" );
document.write( "i took the original equation of -4x^2 + 8x - 3 = 0<BR>\n" );
document.write( "and substituted these values to get:<BR>\n" );
document.write( "0 = 0 both times proving both values are good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "i will do number 30 next and i will leave number 31 for you to do.<BR>\n" );
document.write( "if you follow the steps and understand what is going on, you should be able to complete it.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "equation number 30 is: **************************************************<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+-+8%2Ax+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2+-+8%2Ax+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "standard form of the equation is:<BR>\n" );
document.write( "ax^2 + bx + c = 0<BR>\n" );
document.write( "this is already in standard form.<BR>\n" );
document.write( "a term is -1.<BR>\n" );
document.write( "b term is -8.<BR>\n" );
document.write( "c term is 5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "first you move the constant to the right side of the equation by subtracting 5 from both sides of the equation to get :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+-+8%2Ax+=+-5 ALIGN=MIDDLE  ALT=\"-x%5E2+-+8%2Ax+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then divide both sides of the equation by -1 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+8%2Ax+=+5 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8%2Ax+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take half of 8 and factor the left side of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+4%29%5E2+-+4%5E2+=+5 ALIGN=MIDDLE  ALT=\"%28x+%2B+4%29%5E2+-+4%5E2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then add the 4^2 term to both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2+=+5+%2B+4%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2+=+5+%2B+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then take the square root of both sides of the equation to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4+=+sqrt%285+%2B+4%5E2%29 ALIGN=MIDDLE  ALT=\"x%2B4+=+sqrt%285+%2B+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you then subtract 4 from both sides of the equation to get:<BR>\n" );
document.write( "x = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285+%2B+4%5E2%29-4 ALIGN=MIDDLE  ALT=\"sqrt%285+%2B+4%5E2%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "after doing the math (i used a calculator), you will get:<BR>\n" );
document.write( "x = .5828...<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = =-8.5825...<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to prove these values are correct, substitute them in the original equation (again i used the calculator with the full rather than the truncated values)<BR>\n" );
document.write( "i took the original equation of -x^2 - 8x + 5 = 0 <BR>\n" );
document.write( "and substituted these values to get:<BR>\n" );
document.write( "0 = 0 both times proving both values are good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "by now, you should be able to do number 31 by yourself.<BR>\n" );
document.write( "let me know if you are having problems.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );