document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030563>Question 1030563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why cant you solve x(x + 5) = 24 by solving x = 24 and x + 5 = 24?\r<BR>\n" );
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document.write( "What makes this not possible? Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645410 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=645410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is x * (x + 5) = 24\r<BR>\n" );
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document.write( "you first need to simplify the equation by applying the distributive law of multiplication to get:\r<BR>\n" );
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document.write( "x^2 + 5x = 24\r<BR>\n" );
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document.write( "you then need to subtract 24 from both sides of the equation to get:\r<BR>\n" );
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document.write( "x^2 + 5x - 24 = 0\r<BR>\n" );
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document.write( "you then need to factor this equation to get:\r<BR>\n" );
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document.write( "(x + 8) * (x - 3) = 0\r<BR>\n" );
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document.write( "now that you have the factors equal to 0, you can solve for:\r<BR>\n" );
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document.write( "x + 8 = 0 which results in x = -8\r<BR>\n" );
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document.write( "x - 3 = 0 which results in x = 3.\r<BR>\n" );
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document.write( "why can you do this?\r<BR>\n" );
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document.write( "because 0 * (x-3) = 0 and (x + 8) * 0 = 0\r<BR>\n" );
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document.write( "your original equation was x * (x-5) = 24\r<BR>\n" );
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document.write( "you can't solve it the way you solved the factored quadratic equation because the result is not 0.\r<BR>\n" );
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document.write( "x * (x+5) = 24 won't work.\r<BR>\n" );
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document.write( "if it was x * (x+5) = 0, then it would work.\r<BR>\n" );
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document.write( "but it's not.\r<BR>\n" );
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document.write( "you could subtract 24 from both sides of the equation to get:\r<BR>\n" );
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document.write( "x * (x+5) - 24 = 0\r<BR>\n" );
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document.write( "but you still have to simplify it by using the distributive law of multiplication to get:\r<BR>\n" );
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document.write( "x^2 + 5x - 24 = 0 and then factor that to get (x+8) * (x-3) = 0.\r<BR>\n" );
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document.write( "only then can you separate out the factors and set them equal to 0 and then solve.\r<BR>\n" );
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document.write( "let's assume you could do x * (x+5) = 24 and split it up like:\r<BR>\n" );
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document.write( "x = 24<BR>\n" );
document.write( "x + 5 = 24\r<BR>\n" );
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document.write( "you would get x = 24 or x = 19\r<BR>\n" );
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document.write( "you would then need to confirm if these solutions were correct by replacing x in the original equations.\r<BR>\n" );
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document.write( "when x = 24, x * (x+5) = 24 becomes 24 * 29 = 24 which is clearly not true.\r<BR>\n" );
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document.write( "when x = 19, x * (x+5) = 24 becomes 19 * 24 = 24 which is clearly not true again.\r<BR>\n" );
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document.write( "solving it the right way, you get x = -8 or x = 3\r<BR>\n" );
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document.write( "when x = -8, x * (x+5) = 24 becomes -8 * ( -8 + 5) = 24 which becomes -8 * -3 = 24 which becomes 24 = 24 which is true.\r<BR>\n" );
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document.write( "when x = 3, x * (x+5) = 24 becomes 3 * (3 + 5) = 3 * 8 = 24 which becomes 24 = 24 which is also true.\r<BR>\n" );
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document.write( "breaking up the factors into two separate equations only works when the result is equal to 0.\r<BR>\n" );
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document.write( "x * (x+5) = 0 would work, but x * (x+5) = 24 will not.\r<BR>\n" );
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document.write( "you needed to convert the equation into its quadratic equivalent and then you need to set that equation equal to 0 and then you needed to factor it to get your answer.\r<BR>\n" );
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document.write( "x * (x+5) = 24 becomes x * (x+5) - 24 = 0 which becomes x^2 + 5x - 24 = 0 which is then factored to be (x+8) * (x-3) = 0.\r<BR>\n" );
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document.write( "only then could you set x+8 = 0 and x-3 = 0 to solve for x.\r<BR>\n" );
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