document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113940>Question 113940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the solutions to the equation 4x(squared)-20x= -25 by completing the square. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82915 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=82915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-20x=-25 ALIGN=MIDDLE  ALT=\"4x%5E2-20x=-25\"   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=4%28x%5E2-5x%29=-25 ALIGN=MIDDLE  ALT=\"4%28x%5E2-5x%29=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient 4.  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 -5 to get -2.5 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F2=-2.5 ALIGN=MIDDLE  ALT=\"-5%2F2=-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square -2.5 to get 6.25 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2.5%29%5E2=6.25 ALIGN=MIDDLE  ALT=\"%28-2.5%29%5E2=6.25\"   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=4%28x%5E2-5x%2B6.25%29=-25%2B6.25%284%29 ALIGN=MIDDLE  ALT=\"4%28x%5E2-5x%2B6.25%29=-25%2B6.25%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (6.25) to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x ALIGN=MIDDLE  ALT=\"x%5E2-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  inside the parenthesis. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B6.25 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a perfect square trinomial. Now add the result (6.25)(4) (remember we factored out a 4) to the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-2.5%29%5E2=-25%2B6.25%284%29 ALIGN=MIDDLE  ALT=\"4%28x-2.5%29%5E2=-25%2B6.25%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B6.25 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2.5%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-2.5%29%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=4%28x-2.5%29%5E2=-25%2B25 ALIGN=MIDDLE  ALT=\"4%28x-2.5%29%5E2=-25%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 6.25 and 4 to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-2.5%29%5E2=0 ALIGN=MIDDLE  ALT=\"4%28x-2.5%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2.5%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-2.5%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide 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=x-2.5=0%2B-sqrt%280%29 ALIGN=MIDDLE  ALT=\"x-2.5=0%2B-sqrt%280%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-2.5=0 ALIGN=MIDDLE  ALT=\"x-2.5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of zero to get zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.5 ALIGN=MIDDLE  ALT=\"x=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2.5 to both sides to isolate x.\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.5 ALIGN=MIDDLE  ALT=\"x=2.5\"   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+4x%5E2-20x%2B25%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E2-20x%2B25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%5E2-20x%2B25 ALIGN=MIDDLE  ALT=\"y=4x%5E2-20x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we can see that the x-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.5 ALIGN=MIDDLE  ALT=\"x=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.<BR>\n" );
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