document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870815>Question 870815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the number of solutions of 5x^2-10x-8=0 by using the discriminant.\r<BR>\n" );
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document.write( "Help please, show work please and thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525160 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=525160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax%5E2-10%2Ax-8=0 ALIGN=MIDDLE  ALT=\"5%2Ax%5E2-10%2Ax-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-10 ALIGN=MIDDLE  ALT=\"b=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-8 ALIGN=MIDDLE  ALT=\"c=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=5, b=-10, and c=-8<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -10 to get 10<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100-4%2A5%2A-8+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100-4%2A5%2A-8+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -10 to get 100  (note: remember when you square -10, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29%5E2=-10%2A-10=100 ALIGN=MIDDLE  ALT=\"%28-10%29%5E2=-10%2A-10=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100%2B160+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100%2B160+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-8%2A5 ALIGN=MIDDLE  ALT=\"-4%2A-8%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160 ALIGN=MIDDLE  ALT=\"160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+260+%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+260+%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 5 to get 10<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B+2%2Asqrt%2865%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B+2%2Asqrt%2865%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+-+2%2Asqrt%2865%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%2810+-+2%2Asqrt%2865%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B10%2F10%2B2%2Asqrt%2865%29%2F10 ALIGN=MIDDLE  ALT=\"x=%2B10%2F10%2B2%2Asqrt%2865%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B10%2F10-2%2Asqrt%2865%29%2F10 ALIGN=MIDDLE  ALT=\"x=%2B10%2F10-2%2Asqrt%2865%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2865%29%2F5 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2865%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2865%29%2F5 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2865%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2865%29%2F5 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2865%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2865%29%2F5 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2865%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the discriminant is 260 <BR>\n" );
document.write( "which tells us there are 2 real solutions </SPAN>\n" );
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