document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183223>Question 1183223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve\r<BR>\n" );
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document.write( "factorize <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3x-2 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813431 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the quadratic formula on this one.<BR>\n" );
document.write( "quadratic formula is:<BR>\n" );
document.write( "x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a<BR>\n" );
document.write( "in the equation 2x^2 + 3x - 2, ...<BR>\n" );
document.write( "a = coefficient of x^2 term = 2<BR>\n" );
document.write( "b = coefficient of x term = 3<BR>\n" );
document.write( "c = constant term = 3\r<BR>\n" );
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document.write( "quadratic formula becomes:<BR>\n" );
document.write( "x = (-3 plus or minus sqrt(3^2 - 4*2*-2).<BR>\n" );
document.write( "this becomes x = (-3 plus or minus sqrt(3^2 + 16)) / 4.<BR>\n" );
document.write( "this becomes x = (-3 plus or minus sqrt(25)) / 4.<BR>\n" );
document.write( "this becomes x = (-3 plus or minus 5) / 4.<BR>\n" );
document.write( "this becomes x = 2/4 or -8/4.<BR>\n" );
document.write( "this becomes x = .5 or -2.\r<BR>\n" );
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document.write( "to find the factors, set each of these equations equal to 0 as follows:\r<BR>\n" );
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document.write( "subtract .5 from both sides of the first value of x to get x - .5 = 0<BR>\n" );
document.write( "multiply both sides of that equation to get:<BR>\n" );
document.write( "2x - 1 = 0\r<BR>\n" );
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document.write( "subtract -2 from both sides of the second value of x to get x + 2 = 0\r<BR>\n" );
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document.write( "the factors will be:\r<BR>\n" );
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document.write( "(2x - 1) * (x + 2) = 0\r<BR>\n" );
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document.write( "multiply these factors together to get:\r<BR>\n" );
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document.write( "(2x - 1) * (x + 2) = 2x * (x + 2) - 1 * (x + 2) which becomes:<BR>\n" );
document.write( "2x^2 + 4 - x - 2 which becomes:<BR>\n" );
document.write( "2x^2 + 3x - 2.\r<BR>\n" );
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document.write( "since that is the original equation, the factors look good.\r<BR>\n" );
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document.write( "to confirm that they are the factors, replace x with each value.<BR>\n" );
document.write( "the equation should be equal to 0.\r<BR>\n" );
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document.write( "2x^2 + 3x - 2 becomes 2 * .5^2 + 3 * .5 - 2 when x = .5.<BR>\n" );
document.write( "this becomes 2 * .25 - 1.5 + 2 which becomes:<BR>\n" );
document.write( ".5 - 1.5 + 2 which becomes 0\r<BR>\n" );
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document.write( "2x^2 + 3x - 2 becomes 2 * (-2)^2 + 3 * -2 - 2 when x = -2.<BR>\n" );
document.write( "this becomes 2 * 4 - 6 - 2 which becomes:<BR>\n" );
document.write( "8 - 6 - 2 hich becomes 0,.\r<BR>\n" );
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document.write( "both solution make the equation equal to 0, confirming they are the correct solutions.\r<BR>\n" );
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document.write( "with quadratic equations, your fallback position is the quadratic formula.<BR>\n" );
document.write( "use of that formula will always provide the solutions, whether they are real or not.\r<BR>\n" );
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document.write( "here's a reference on how to solve quadratic equations.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/solvquad6.htm\" target = \"_blank\">https://www.purplemath.com/modules/solvquad6.htm</a.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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