document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102791>Question 102791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 24x²-2x=15  solve the equation by factoring and quadratic formula </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74796 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=74796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"24x²-2x=15  solve the equation by factoring\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x%5E2-2x=15 ALIGN=MIDDLE  ALT=\"24x%5E2-2x=15\"   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=24x%5E2-2x-15=0 ALIGN=MIDDLE  ALT=\"24x%5E2-2x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 15 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-5%29%284x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%286x-5%29%284x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-5=0 ALIGN=MIDDLE  ALT=\"6x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3=0 ALIGN=MIDDLE  ALT=\"4x%2B3=0\"   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=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now solve for x in each case\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=x=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24x%5E2-2x-15 ALIGN=MIDDLE  ALT=\"y=24x%5E2-2x-15\"   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%28500%2C500%2C-10%2C10%2C-10%2C10%2C+24x%5E2-2x-15%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+24x%5E2-2x-15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the graph has roots at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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document.write( "\"4x²-2x=15  solve the equation by the quadratic formula\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x%5E2-2x=15 ALIGN=MIDDLE  ALT=\"24x%5E2-2x=15\"   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=24x%5E2-2x-15=0 ALIGN=MIDDLE  ALT=\"24x%5E2-2x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 15 from both sides\r<BR>\n" );
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document.write( "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( "<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;\" >\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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Ax%5E2-2%2Ax-15=0 ALIGN=MIDDLE  ALT=\"24%2Ax%5E2-2%2Ax-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=24 ALIGN=MIDDLE  ALT=\"a=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-15 ALIGN=MIDDLE  ALT=\"c=-15\"   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--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A24%2A-15+%29%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A24%2A-15+%29%29%2F%282%2A24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=24, b=-2, and c=-15\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A24%2A-15+%29%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A24%2A-15+%29%29%2F%282%2A24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -2 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+4-4%2A24%2A-15+%29%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+4-4%2A24%2A-15+%29%29%2F%282%2A24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -2 to get 4  (note: remember when you square -2, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E2=-2%2A-2=4 ALIGN=MIDDLE  ALT=\"%28-2%29%5E2=-2%2A-2=4\"   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+=+%282+%2B-+sqrt%28+4%2B1440+%29%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+4%2B1440+%29%29%2F%282%2A24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-15%2A24 ALIGN=MIDDLE  ALT=\"-4%2A-15%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1440 ALIGN=MIDDLE  ALT=\"1440\"   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+=+%282+%2B-+sqrt%28+1444+%29%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+1444+%29%29%2F%282%2A24%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+=+%282+%2B-+38%29%2F%282%2A24%29 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+38%29%2F%282%2A24%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>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+38%29%2F48 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+38%29%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 24 to get 48\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=x+=+%282+%2B+38%29%2F48 ALIGN=MIDDLE  ALT=\"x+=+%282+%2B+38%29%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+-+38%29%2F48 ALIGN=MIDDLE  ALT=\"x+=+%282+-+38%29%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282+%2B+38%29%2F48 ALIGN=MIDDLE  ALT=\"x=%282+%2B+38%29%2F48\"   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=40%2F48 ALIGN=MIDDLE  ALT=\"x=40%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282+-+38%29%2F48 ALIGN=MIDDLE  ALT=\"x=%282+-+38%29%2F48\"   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=-36%2F48 ALIGN=MIDDLE  ALT=\"x=-36%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "So our solutions are:\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=24%2Ax%5E2-2%2Ax-15 ALIGN=MIDDLE  ALT=\"24%2Ax%5E2-2%2Ax-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "and we can see that the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F6 ALIGN=MIDDLE  ALT=\"x=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This verifies our answer\r<BR>\n" );
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document.write( " </SPAN>\n" );
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