document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101192>Question 101192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x^2+2x-3=0. Solve by completing the square. (4x^2 is 4x squared) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73649 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=73649\">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%2B2x-3=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B2x-3=0\"   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=4x%5E2%2B2x=3 ALIGN=MIDDLE  ALT=\"4x%5E2%2B2x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2%2B0.5x%29=3 ALIGN=MIDDLE  ALT=\"4%28x%5E2%2B0.5x%29=3\"   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 0.5 to get 0.25 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2F2=0.25 ALIGN=MIDDLE  ALT=\"0.5%2F2=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square 0.25 to get 0.0625 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.25%29%5E2=0.0625 ALIGN=MIDDLE  ALT=\"%280.25%29%5E2=0.0625\"   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%2B0.5x%2B0.0625%29=3%2B0.0625%284%29 ALIGN=MIDDLE  ALT=\"4%28x%5E2%2B0.5x%2B0.0625%29=3%2B0.0625%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (0.0625) to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B0.5x ALIGN=MIDDLE  ALT=\"x%5E2%2B0.5x\"   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%2B0.5x%2B0.0625 ALIGN=MIDDLE  ALT=\"x%5E2%2B0.5x%2B0.0625\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a perfect square trinomial. Now add the result (0.0625)(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%2B0.25%29%5E2=3%2B0.0625%284%29 ALIGN=MIDDLE  ALT=\"4%28x%2B0.25%29%5E2=3%2B0.0625%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B0.5x%2B0.0625 ALIGN=MIDDLE  ALT=\"x%5E2%2B0.5x%2B0.0625\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B0.25%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B0.25%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%2B0.25%29%5E2=3%2B0.25 ALIGN=MIDDLE  ALT=\"4%28x%2B0.25%29%5E2=3%2B0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 0.0625 and 4 to get 0.25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B0.25%29%5E2=3.25 ALIGN=MIDDLE  ALT=\"4%28x%2B0.25%29%5E2=3.25\"   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%2B0.25%29%5E2=0.8125 ALIGN=MIDDLE  ALT=\"%28x%2B0.25%29%5E2=0.8125\"   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%2B0.25=0%2B-sqrt%280.8125%29 ALIGN=MIDDLE  ALT=\"x%2B0.25=0%2B-sqrt%280.8125%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=-0.25%2B-sqrt%280.8125%29 ALIGN=MIDDLE  ALT=\"x=-0.25%2B-sqrt%280.8125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 0.25 from both sides to isolate x.\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=-0.25%2Bsqrt%280.8125%29 ALIGN=MIDDLE  ALT=\"x=-0.25%2Bsqrt%280.8125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.25-sqrt%280.8125%29 ALIGN=MIDDLE  ALT=\"x=-0.25-sqrt%280.8125%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=0.651387818865997 ALIGN=MIDDLE  ALT=\"x=0.651387818865997\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.151387818866 ALIGN=MIDDLE  ALT=\"x=-1.151387818866\"   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%2B2x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E2%2B2x-3%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%2B2x-3 ALIGN=MIDDLE  ALT=\"y=4x%5E2%2B2x-3\"   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=0.651387818865997 ALIGN=MIDDLE  ALT=\"x=0.651387818865997\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.151387818866 ALIGN=MIDDLE  ALT=\"x=-1.151387818866\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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