document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115722>Question 115722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a test tomorrow and am having a lot of trouble with quadratic equations. i understand some things, but others do not make sense at all. below are 3 problems that i do not understand how to solve. if you could solve the problem and show the steps, that would really help me a lot. \r<BR>\n" );
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document.write( "1. 2x^2 - 14x - 10 = 0  (must be solved by factoring or by completing the square, cannot use the quadratic formula)\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 #84200 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=84200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-14x-10=0 ALIGN=MIDDLE  ALT=\"2x%5E2-14x-10=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=2x%5E2-14x=10 ALIGN=MIDDLE  ALT=\"2x%5E2-14x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 10 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-7x%29=10 ALIGN=MIDDLE  ALT=\"2%28x%5E2-7x%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient 2.  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 -7 to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2 ALIGN=MIDDLE  ALT=\"-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2 ALIGN=MIDDLE  ALT=\"-7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F4 ALIGN=MIDDLE  ALT=\"49%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=2%28x%5E2-7x%2B49%2F4%29=10%2B%2849%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-7x%2B49%2F4%29=10%2B%2849%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (12.25) to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x ALIGN=MIDDLE  ALT=\"x%5E2-7x\"   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%5E2-7x%2B49%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-7x%2B49%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a perfect square trinomial. Now add the result <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2849%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"%2849%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we factored out a 2) 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=2%28x-7%2F2%29%5E2=10%2B%2849%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"2%28x-7%2F2%29%5E2=10%2B%2849%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x%2B49%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-7x%2B49%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-7%2F2%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=2%28x-7%2F2%29%5E2=10%2B49%2F2 ALIGN=MIDDLE  ALT=\"2%28x-7%2F2%29%5E2=10%2B49%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F4 ALIGN=MIDDLE  ALT=\"49%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F2 ALIGN=MIDDLE  ALT=\"49%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=2%28x-7%2F2%29%5E2=69%2F2 ALIGN=MIDDLE  ALT=\"2%28x-7%2F2%29%5E2=69%2F2\"   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-7%2F2%29%5E2=69%2F4 ALIGN=MIDDLE  ALT=\"%28x-7%2F2%29%5E2=69%2F4\"   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-7%2F2=0%2B-sqrt%2869%2F4%29 ALIGN=MIDDLE  ALT=\"x-7%2F2=0%2B-sqrt%2869%2F4%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-7%2F2=0%2B-sqrt%2869%29%2F2 ALIGN=MIDDLE  ALT=\"x-7%2F2=0%2B-sqrt%2869%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F2%2B-sqrt%2869%29%2F2 ALIGN=MIDDLE  ALT=\"x=7%2F2%2B-sqrt%2869%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2 ALIGN=MIDDLE  ALT=\"7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%287%2B-sqrt%2869%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%287%2B-sqrt%2869%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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