document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135087>Question 135087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,I was wondering if anyone could help me solve this equation? I'm having trouble with it.<BR>\n" );
document.write( "x^2-3x=18 the directions are to solve the equation.\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Mrs. Gibson </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98926 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=98926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well in order to solve a quadratic equation we first must have it in standard form.  Standard form is ax^2+bx+c = 0 where a, b, and c are numbers.  <br>\r<BR>\n" );
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document.write( "so putting the function into standard form you get:<br>\r<BR>\n" );
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document.write( "x^2-3x=18<BR>\n" );
document.write( "x^2-3x-18=0<br>\r<BR>\n" );
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document.write( "now we need to factor.  The steps to factoring are:<BR>\n" );
document.write( "1) Multiply a times c <BR>\n" );
document.write( "2) See what factors of the number found in step one add to the b value<BR>\n" );
document.write( "3) break the function into a product of its factors<br>\r<BR>\n" );
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document.write( "In this example a = 1, b = -3, and c = -18.  So a*c = -18.  So we need to find the factors of -18 that add to -3. Well the factors of 18 are:<br>\r<BR>\n" );
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document.write( "1,-18<BR>\n" );
document.write( "2,-9<BR>\n" );
document.write( "3,-6<br>\r<BR>\n" );
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document.write( "well -6+3 = -3 so those are the factors we wanted.<br>\r<BR>\n" );
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document.write( "So we now know that x^2-3x-18 can be written as (x-6)(x+3).  This is now in factored form.<br>\r<BR>\n" );
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document.write( "Now we use the zero product property that states that you can set each one of those factors equal to zero and solve for x.<br>\r<BR>\n" );
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document.write( "x-6 = 0 <BR>\n" );
document.write( "x = 6<br>\r<BR>\n" );
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document.write( "x+3 = 0<BR>\n" );
document.write( "x = -3<br>\r<BR>\n" );
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document.write( "so now we know that the solutions to the given equation are x = -3 and x = 6.<br>\r<BR>\n" );
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document.write( "Now to check our solutions:<br>\r<BR>\n" );
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document.write( "x^2-3x-18 = 0<BR>\n" );
document.write( "(6)^2-3(6)-18=0<BR>\n" );
document.write( "36 - 18 - 18 = 0<BR>\n" );
document.write( "36 - 36 = 0<BR>\n" );
document.write( "0 = 0  <br>\r<BR>\n" );
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document.write( "that solution checks out now lets check the other one<br>\r<BR>\n" );
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document.write( "x^2-3x-18 = 0<BR>\n" );
document.write( "(-3)^2 - 3(-3) - 18 = 0<BR>\n" );
document.write( "9 + 9 - 18 = 0<BR>\n" );
document.write( "18 - 18 = 0<BR>\n" );
document.write( "0 = 0<br>\r<BR>\n" );
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document.write( "that solution also check's out. </SPAN>\n" );
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