document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171112>Question 171112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x^2-2x+7=0 \r<BR>\n" );
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document.write( "I have to solve this by completing the square. I solved it but I'm unsure of my answer, I got x= 1/2 + or - i times radical 13 over 2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126321 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Complete the square on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-2x%2B7=0 ALIGN=MIDDLE  ALT=\"2x%5E2-2x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1, starting from a quadratic in standard form like you have is to put the constant term on the right:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-2x=-7 ALIGN=MIDDLE  ALT=\"2x%5E2-2x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2, if the coefficient on 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;\" > term is other than 1, divide by that coefficient.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=-7%2F2 ALIGN=MIDDLE  ALT=\"x%5E2-x=-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3, divide the resulting coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > term by 2 and square the result\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-1%29%2F2%29%5E2=1%2F4 ALIGN=MIDDLE  ALT=\"%28%28-1%29%2F2%29%5E2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4, add this result to both sides of your equation and collect terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2B1%2F4=-7%2F2%2B1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=-7%2F2%2B1%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%5E2-x%2B1%2F4=-13%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=-13%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5, the above result has a perfect square on the left (hence the term \"completing the square\"), so factor it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F2%29%5E2=-13%2F4 ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2=-13%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6, 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%2F2=sqrt%28-13%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=sqrt%28-13%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=-sqrt%28-13%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=-sqrt%28-13%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which leads us to a great big oops! because you can't take the square root of a negative number.  The solution is to use the imaginary number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is defined as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, leaving us with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=sqrt%28%28-1%2913%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=sqrt%28%28-1%2913%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=-sqrt%28%28-1%2913%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=-sqrt%28%28-1%2913%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=sqrt%28-1%29%2Asqrt%2813%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=sqrt%28-1%29%2Asqrt%2813%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=-sqrt%28-1%29%2Asqrt%2813%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=-sqrt%28-1%29%2Asqrt%2813%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=i%2Asqrt%2813%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=i%2Asqrt%2813%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=-i%2Asqrt%2813%2F4%29 ALIGN=MIDDLE  ALT=\"x-1%2F2=-i%2Asqrt%2813%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7, isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify in each equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=1%2F2%2Bi%2Asqrt%2813%2F4%29=%281%2Bi%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=1%2F2%2Bi%2Asqrt%2813%2F4%29=%281%2Bi%2Asqrt%2813%29%29%2F2\"   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%5B2%5D=1%2F2-i%2Asqrt%2813%2F4%29=%281-i%2Asqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=1%2F2-i%2Asqrt%2813%2F4%29=%281-i%2Asqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you want the exact representation of the roots of the given equation, you are done.  If you need a numerical approximation of the imaginary parts of your complex numbers, get out your calculator.\r<BR>\n" );
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document.write( "Multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-%28%281%2Bi%2Asqrt%2813%29%29%2F2%29%29%28x-%28%281-i%2Asqrt%2813%29%29%2F2%29%29 ALIGN=MIDDLE  ALT=\"+%28x-%28%281%2Bi%2Asqrt%2813%29%29%2F2%29%29%28x-%28%281-i%2Asqrt%2813%29%29%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to verify that the product is, in fact, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-2x%2B7 ALIGN=MIDDLE  ALT=\"2x%5E2-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is left as an exercise for the student.  Alternatively, you could just trust me.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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