document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857325>Question 857325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me figure out what the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 3x + 7.  I know I can graph it to find the answers, but I am not sure how to even work the problem out to get to the graphing. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516494 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=516494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 0 = -3x2 + 3x + 7\r<BR>\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( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Ax%5E2%2B3%2Ax%2B7=0 ALIGN=MIDDLE  ALT=\"-3%2Ax%5E2%2B3%2Ax%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-3 ALIGN=MIDDLE  ALT=\"a=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7 ALIGN=MIDDLE  ALT=\"c=7\"   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+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A-3%2A7+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A-3%2A7+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-3, b=3, and c=7<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9-4%2A-3%2A7+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9-4%2A-3%2A7+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 3 to get 9  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9%2B84+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9%2B84+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A7%2A-3 ALIGN=MIDDLE  ALT=\"-4%2A7%2A-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   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+=+%28-3+%2B-+sqrt%28+93+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+93+%29%29%2F%282%2A-3%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+=+%28-3+%2B-+sqrt%2893%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%2893%29%29%2F%282%2A-3%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+=+%28-3+%2B-+sqrt%2893%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%2893%29%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -3 to get -6<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+=+%28-3+%2B+sqrt%2893%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B+sqrt%2893%29%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+-+sqrt%2893%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-3+-+sqrt%2893%29%29%2F-6\"   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=-3%2F-6%2Bsqrt%2893%29%2F-6 ALIGN=MIDDLE  ALT=\"x=-3%2F-6%2Bsqrt%2893%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F-6-sqrt%2893%29%2F-6 ALIGN=MIDDLE  ALT=\"x=-3%2F-6-sqrt%2893%29%2F-6\"   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%2F2-sqrt%2893%29%2F6 ALIGN=MIDDLE  ALT=\"x=1%2F2-sqrt%2893%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2%2Bsqrt%2893%29%2F6 ALIGN=MIDDLE  ALT=\"x=1%2F2%2Bsqrt%2893%29%2F6\"   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%2F2-sqrt%2893%29%2F6 ALIGN=MIDDLE  ALT=\"x=1%2F2-sqrt%2893%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2%2Bsqrt%2893%29%2F6 ALIGN=MIDDLE  ALT=\"x=1%2F2%2Bsqrt%2893%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x = 1/6 (3-sqrt(93)) x = -1.1073<BR>\n" );
document.write( "x = 1/6 (3+sqrt(93)) x = 2.1073 </SPAN>\n" );
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