document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449355>Question 449355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me use the zero property or factoring to find the solution of (x+2)(2x+7)=-15 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309110 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=309110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadratic Equation in Standard Form\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Zero Factor Property\r<BR>\n" );
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document.write( "If a product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab+=+0 ALIGN=MIDDLE  ALT=\"ab+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+0 ALIGN=MIDDLE  ALT=\"a+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+0 ALIGN=MIDDLE  ALT=\"b+=+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=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our magic number because the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" > way a product can become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is if at least one of its factors is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you need:\r<BR>\n" );
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document.write( "use the zero property or factoring to find the solution of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%282x%2B7%29=-15+ ALIGN=MIDDLE  ALT=\"%28x%2B2%29%282x%2B7%29=-15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....first set equation = to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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=%28x%2B2%29%282x%2B7%29%2B15=0+ ALIGN=MIDDLE  ALT=\"%28x%2B2%29%282x%2B7%29%2B15=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%2B7x%2B14%2B15=0+ ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2B7x%2B14%2B15=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=2x%5E2%2B11x%2B29=0+ ALIGN=MIDDLE  ALT=\"2x%5E2%2B11x%2B29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B11x%2B29=0+ ALIGN=MIDDLE  ALT=\"2x%5E2%2B11x%2B29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be factored,. ... you cannot  find the solution of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%282x%2B7%29=-15+ ALIGN=MIDDLE  ALT=\"%28x%2B2%29%282x%2B7%29=-15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > by using the zero property or factoring\r<BR>\n" );
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document.write( "only way is to use quadratic formula \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( "  <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=2%2Ax%5E2%2B11%2Ax%2B29=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B11%2Ax%2B29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=11 ALIGN=MIDDLE  ALT=\"b=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=29 ALIGN=MIDDLE  ALT=\"c=29\"   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+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A2%2A29+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A2%2A29+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=11, and c=29<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+%2B-+sqrt%28+121-4%2A2%2A29+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+121-4%2A2%2A29+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 11 to get 121  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+%2B-+sqrt%28+121%2B-232+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+121%2B-232+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A29%2A2 ALIGN=MIDDLE  ALT=\"-4%2A29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-232 ALIGN=MIDDLE  ALT=\"-232\"   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+=+%28-11+%2B-+sqrt%28+-111+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+sqrt%28+-111+%29%29%2F%282%2A2%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+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%282%2A2%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+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4<BR>\n" );
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document.write( "  After simplifying, the quadratic has roots of<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-11%2F4%2Bsqrt%28111%29%2F4%2Ai ALIGN=MIDDLE  ALT=\"x=-11%2F4%2Bsqrt%28111%29%2F4%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-11%2F4-sqrt%28111%29%2F4%2Ai ALIGN=MIDDLE  ALT=\"x=-11%2F4-sqrt%28111%29%2F4%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "as you can see, there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NO ALIGN=MIDDLE  ALT=\"NO\"   DISABLED_style= \"max-width:90%; height:auto;\" > real solutions, only imaginary solutions\r<BR>\n" );
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