document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92078>Question 92078</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this quadratic equation, Solve using completing the square, 3x^2 - 6x = 27\r<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 #66922 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=66922\">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=3%28x%5E2-2x%29=27 ALIGN=MIDDLE  ALT=\"3%28x%5E2-2x%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient 3. This step is important since we want the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient to be equal to 1.\r<BR>\n" );
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document.write( "Take half of the x coefficient -2 to get -1 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F2=-1 ALIGN=MIDDLE  ALT=\"-2%2F2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square -1 to get 1 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28-1%29%5E2=1\"   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=3%28x%5E2-2x%2B1%29=27 ALIGN=MIDDLE  ALT=\"3%28x%5E2-2x%2B1%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (1) to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x ALIGN=MIDDLE  ALT=\"x%5E2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  inside the parenthesis\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-2x%2B1%29=27%2B1%283%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2-2x%2B1%29=27%2B1%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1(3) to the other side (remember we factored out a 3)\r<BR>\n" );
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document.write( "Now the left side is a complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%29%5E2=27%2B1%283%29 ALIGN=MIDDLE  ALT=\"3%28x-1%29%5E2=27%2B1%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%29%5E2=27%2B3 ALIGN=MIDDLE  ALT=\"3%28x-1%29%5E2=27%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 1 and 3 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%29%5E2=30 ALIGN=MIDDLE  ALT=\"3%28x-1%29%5E2=30\"   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=%28x-1%29%5E2=10 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=0%2B-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x-1=0%2B-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2B-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=1%2B-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides\r<BR>\n" );
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document.write( "So the expression breaks down to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.16227766016838 ALIGN=MIDDLE  ALT=\"x=4.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.16227766016838 ALIGN=MIDDLE  ALT=\"x=-2.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is visual proof\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E2-6x-27%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E2-6x-27%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%5E2-6x-27 ALIGN=MIDDLE  ALT=\"y=3x%5E2-6x-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When we use the root finder feature on a calculator, we would find that the x-intercepts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.16227766016838 ALIGN=MIDDLE  ALT=\"x=4.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.16227766016838 ALIGN=MIDDLE  ALT=\"x=-2.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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