document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104710>Question 104710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x-2*sqrt(x-3)=3\r<BR>\n" );
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document.write( "solve for zero...\r<BR>\n" );
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document.write( "I subtract x from both sides which =\r<BR>\n" );
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document.write( "-2*sqrt(x-3)=3-x\r<BR>\n" );
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document.write( "then I divide by -2 from both sides\r<BR>\n" );
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document.write( "sqrt(x-3)=(3-x)/-2\r<BR>\n" );
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document.write( "then to get rid of the \"sqrt\"  ^2 on both sides\r<BR>\n" );
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document.write( "x-3=(9+x^2)/4\r<BR>\n" );
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document.write( "then I subtract \"x\" and add 3 to both sides to solve for zero.\r<BR>\n" );
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document.write( "0=(9+x^2)/4-x+3\r<BR>\n" );
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document.write( "then I find a common denominator of 4 and solve\r<BR>\n" );
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document.write( "0=(9+x^2)/4 -4x/4+12/4 which equals 0=(x^2-4x+21)/4\r<BR>\n" );
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document.write( "then I multiply 4/1 on both side the loose the denominator.\r<BR>\n" );
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document.write( "0=x^2-4x+21 which can not be factored, but my text book gives a solution set of {7,3}. I cant find were I went wrong, please help.<BR>\n" );
document.write( "Please note, this question had already been answered but the link to the answer did not work so this is why I am re-submitting it. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76202 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=76202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%2Asqrt%28x-3%29=3 ALIGN=MIDDLE  ALT=\"x-2%2Asqrt%28x-3%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asqrt%28x-3%29=3-x ALIGN=MIDDLE  ALT=\"-2%2Asqrt%28x-3%29=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29=%283-x%29%2F-2 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29=%283-x%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=%28%283-x%29%2F-2%29%5E2 ALIGN=MIDDLE  ALT=\"x-3=%28%283-x%29%2F-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "Now this is where you went wrong, when you square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-x ALIGN=MIDDLE  ALT=\"3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > you need to foil it to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-6x%2Bx%5E2 ALIGN=MIDDLE  ALT=\"9-6x%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Bx%5E2 ALIGN=MIDDLE  ALT=\"9%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=%289-6x%2Bx%5E2%29%2F4 ALIGN=MIDDLE  ALT=\"x-3=%289-6x%2Bx%5E2%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the numerator and square the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%289-6x%2Bx%5E2%29%2F4%2B3 ALIGN=MIDDLE  ALT=\"x=%289-6x%2Bx%5E2%29%2F4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%289-6x%2Bx%5E2%29%2F4%2B3%284%2F4%29 ALIGN=MIDDLE  ALT=\"x=%289-6x%2Bx%5E2%29%2F4%2B3%284%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%289-6x%2Bx%5E2%29%2F4%2B12%2F4 ALIGN=MIDDLE  ALT=\"x=%289-6x%2Bx%5E2%29%2F4%2B12%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%289-6x%2Bx%5E2%2B12%29%2F4 ALIGN=MIDDLE  ALT=\"x=%289-6x%2Bx%5E2%2B12%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-6x%2Bx%5E2%2B21%29%2F4 ALIGN=MIDDLE  ALT=\"x=%28-6x%2Bx%5E2%2B21%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=-6x%2Bx%5E2%2B21 ALIGN=MIDDLE  ALT=\"4x=-6x%2Bx%5E2%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-6x%2Bx%5E2%2B21-4x ALIGN=MIDDLE  ALT=\"0=-6x%2Bx%5E2%2B21-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B21-10x ALIGN=MIDDLE  ALT=\"0=x%5E2%2B21-10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-10x%2B21 ALIGN=MIDDLE  ALT=\"0=x%5E2-10x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\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_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <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;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<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 lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10%2Ax%2B21=0 ALIGN=MIDDLE  ALT=\"x%5E2-10%2Ax%2B21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-10 ALIGN=MIDDLE  ALT=\"b=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=21 ALIGN=MIDDLE  ALT=\"c=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A21+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A21+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-10, and c=21<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A21+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A21+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -10 to get 10<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A21+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A21+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -10 to get 100  (note: remember when you square -10, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29%5E2=-10%2A-10=100 ALIGN=MIDDLE  ALT=\"%28-10%29%5E2=-10%2A-10=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100%2B-84+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100%2B-84+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A21%2A1 ALIGN=MIDDLE  ALT=\"-4%2A21%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-84 ALIGN=MIDDLE  ALT=\"-84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+4%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+4%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+4%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B+4%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B+4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+-+4%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2810+-+4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2810+%2B+4%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2810+%2B+4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=14%2F2 ALIGN=MIDDLE  ALT=\"x=14%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2810+-+4%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2810+-+4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2F2 ALIGN=MIDDLE  ALT=\"x=6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  So our solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So this means the solution set is {7,3} </SPAN>\n" );
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