document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88512>Question 88512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the quadratic formula to solve z^2-8z=-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64350 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=64350\">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=z%5E2-8z=-5 ALIGN=MIDDLE  ALT=\"z%5E2-8z=-5\"   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=z%5E2-8z%2B5=0 ALIGN=MIDDLE  ALT=\"z%5E2-8z%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5 to both sides\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for z:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=az%5E2%2Bbz%2Bc=0 ALIGN=MIDDLE  ALT=\"az%5E2%2Bbz%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-8%2Az%2B5=0 ALIGN=MIDDLE  ALT=\"z%5E2-8%2Az%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   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=z+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-8, and c=5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -8 to get 8\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B-+sqrt%28+64-4%2A1%2A5+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+sqrt%28+64-4%2A1%2A5+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -8 to get 64\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B-+sqrt%28+64%2B-20+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+sqrt%28+64%2B-20+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A5%2A1 ALIGN=MIDDLE  ALT=\"-4%2A5%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20 ALIGN=MIDDLE  ALT=\"-20\"   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=z+=+%288+%2B-+sqrt%28+44+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+sqrt%28+44+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B-+2%2Asqrt%2811%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+2%2Asqrt%2811%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B-+2%2Asqrt%2811%29%29%2F2 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B-+2%2Asqrt%2811%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+%2B+2%2Asqrt%2811%29%29%2F2 ALIGN=MIDDLE  ALT=\"z+=+%288+%2B+2%2Asqrt%2811%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288+-+2%2Asqrt%2811%29%29%2F2 ALIGN=MIDDLE  ALT=\"z+=+%288+-+2%2Asqrt%2811%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=7.3166247903554 ALIGN=MIDDLE  ALT=\"z=7.3166247903554\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=0.6833752096446 ALIGN=MIDDLE  ALT=\"z=0.6833752096446\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=7.3166247903554 ALIGN=MIDDLE  ALT=\"z=7.3166247903554\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=0.6833752096446 ALIGN=MIDDLE  ALT=\"z=0.6833752096446\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8%2Ax%2B5 ALIGN=MIDDLE  ALT=\"x%5E2-8%2Ax%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace z with x), we get:\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+-9.3166247903554%2C+17.3166247903554%2C+-9.3166247903554%2C+17.3166247903554%2C1%2Ax%5E2%2B-8%2Ax%2B5%29+ ALIGN=MIDDLE   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 find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.3166247903554 ALIGN=MIDDLE  ALT=\"x=7.3166247903554\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.6833752096446 ALIGN=MIDDLE  ALT=\"x=0.6833752096446\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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