document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89372>Question 89372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by using the quadratic formula\r<BR>\n" );
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document.write( "4x^2-3x+3=0\r<BR>\n" );
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document.write( "Having trouble any help appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64978 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=64978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\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=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;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%5E2-3%2Ax%2B3=0 ALIGN=MIDDLE  ALT=\"4%2Ax%5E2-3%2Ax%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   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=3 ALIGN=MIDDLE  ALT=\"c=3\"   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+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=4, b=-3, and c=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -3 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+9-4%2A4%2A3+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+9-4%2A4%2A3+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -3 to get 9  (note: remember when you square -3, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%5E2=-3%2A-3=9 ALIGN=MIDDLE  ALT=\"-3%5E2=-3%2A-3=9\"   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+=+%283+%2B-+sqrt%28+9%2B-48+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+9%2B-48+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A3%2A4 ALIGN=MIDDLE  ALT=\"-4%2A3%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   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+=+%283+%2B-+sqrt%28+-39+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%282%2A4%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=x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: since we cannot take the square root of a negative value, we must factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-39%29 ALIGN=MIDDLE  ALT=\"sqrt%28-39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%2839%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%2839%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make the radicand positive. 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>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 4 to get 8\r<BR>\n" );
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document.write( "After simplifying, the quadratic has roots of\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F8+%2B+sqrt%2839%29%2F8%2Ai ALIGN=MIDDLE  ALT=\"x=3%2F8+%2B+sqrt%2839%29%2F8%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F8+-+sqrt%2839%29%2F8%2Ai ALIGN=MIDDLE  ALT=\"x=3%2F8+-+sqrt%2839%29%2F8%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Ax%5E2-3%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=4%2Ax%5E2-3%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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+-14.625%2C+15.375%2C+-12.5625%2C+17.4375%2C+4%2Ax%5E2-3%2Ax%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-14.625%2C+15.375%2C+-12.5625%2C+17.4375%2C+4%2Ax%5E2-3%2Ax%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Ax%5E2-3%2Ax%2B3 ALIGN=MIDDLE  ALT=\"y=4%2Ax%5E2-3%2Ax%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To visually verify the answer, check out <a  rel=nofollow HREF=http://www.math.hmc.edu/funfacts/ffiles/10005.1.shtml>this page</a> to see a visual representation of imaginary roots<BR>\n" );
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