document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91863>Question 91863</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> can you please help me solve this equation  12x^2 + 7 =10 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66731 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=66731\">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=12x%5E2+%2B+7x+=10 ALIGN=MIDDLE  ALT=\"12x%5E2+%2B+7x+=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > I'm assuming it looks like this right?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2+%2B+7x+-10=0 ALIGN=MIDDLE  ALT=\"12x%5E2+%2B+7x+-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 10 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( "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=12%2Ax%5E2%2B7%2Ax-10=0 ALIGN=MIDDLE  ALT=\"12%2Ax%5E2%2B7%2Ax-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=12 ALIGN=MIDDLE  ALT=\"a=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-10 ALIGN=MIDDLE  ALT=\"c=-10\"   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+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A12%2A-10+%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A12%2A-10+%29%29%2F%282%2A12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=12, b=7, and c=-10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%28+49-4%2A12%2A-10+%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49-4%2A12%2A-10+%29%29%2F%282%2A12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 7 to get 49  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+%2B-+sqrt%28+49%2B480+%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+49%2B480+%29%29%2F%282%2A12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-10%2A12 ALIGN=MIDDLE  ALT=\"-4%2A-10%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480 ALIGN=MIDDLE  ALT=\"480\"   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+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%282%2A12%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+=+%28-7+%2B-+23%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+23%29%2F%282%2A12%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+=+%28-7+%2B-+23%29%2F24 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B-+23%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 12 to get 24\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+=+%28-7+%2B+23%29%2F24 ALIGN=MIDDLE  ALT=\"x+=+%28-7+%2B+23%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7+-+23%29%2F24 ALIGN=MIDDLE  ALT=\"x+=+%28-7+-+23%29%2F24\"   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=%28-7+%2B+23%29%2F24 ALIGN=MIDDLE  ALT=\"x=%28-7+%2B+23%29%2F24\"   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=16%2F24 ALIGN=MIDDLE  ALT=\"x=16%2F24\"   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=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   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=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   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=%28-7+-+23%29%2F24 ALIGN=MIDDLE  ALT=\"x=%28-7+-+23%29%2F24\"   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=-30%2F24 ALIGN=MIDDLE  ALT=\"x=-30%2F24\"   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=-5%2F4 ALIGN=MIDDLE  ALT=\"x=-5%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F4 ALIGN=MIDDLE  ALT=\"x=-5%2F4\"   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( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ax%5E2%2B7%2Ax-10 ALIGN=MIDDLE  ALT=\"12%2Ax%5E2%2B7%2Ax-10\"   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=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F4 ALIGN=MIDDLE  ALT=\"x=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This verifies our answer </SPAN>\n" );
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