document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124943>Question 124943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you solve this equation?\r<BR>\n" );
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document.write( "a^2-3=2a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91585 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=91585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "a^2 - 3 = 2a<BR>\n" );
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document.write( "To solve this, begin by getting it into a standard quadratic form in which the right side<BR>\n" );
document.write( "of the equation equals zero. To do this you just need to subtract 2a from both sides of<BR>\n" );
document.write( "the equation. This subtraction makes the equation become:<BR>\n" );
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document.write( "a^2 - 2a - 3 = 0<BR>\n" );
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document.write( "The left side of this equation can be factored into two binomials. When you factor the left side<BR>\n" );
document.write( "the equation is transformed to:<BR>\n" );
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document.write( "(a - 3)(a + 1) = 0<BR>\n" );
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document.write( "[Notice that if you multiply out the two binomials factors on the left side you get back to <BR>\n" );
document.write( "a^2 - 2a - 3 = 0]<BR>\n" );
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document.write( "This equation will be true if either of the two binomial factors is equal to zero because<BR>\n" );
document.write( "multiplying the two factors (when one of them is zero) will make the entire left side of the<BR>\n" );
document.write( "equation be equal to zero and therefore the left side will be equal to the zero on the right side.<BR>\n" );
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document.write( "So, one at a time set the two factors equal to zero. First:<BR>\n" );
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document.write( "a - 3 = 0<BR>\n" );
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document.write( "Solve for a by adding 3 to both sides of this equation and you get a = 3.<BR>\n" );
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document.write( "Next, set the second factor equal to zero:<BR>\n" );
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document.write( "a + 1 = 0<BR>\n" );
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document.write( "Solve for a by subtracting 1 from both sides to get:<BR>\n" );
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document.write( "a = -1<BR>\n" );
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document.write( "That is the second answer. The two answers are a = 3 and a = -1<BR>\n" );
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document.write( "You can check these answers by returning to the original problem:<BR>\n" );
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document.write( "a^2 - 3 = 2a<BR>\n" );
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document.write( "and, one at a time substitute the answers to see if the left side of the equation will<BR>\n" );
document.write( "equal to the right side.<BR>\n" );
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document.write( "Check a = 3 by substituting 3 for a in the original problem and you get:<BR>\n" );
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document.write( "3^2 - 3 = 2*3<BR>\n" );
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document.write( "Square the 3 and subtract 3 from it on the left side and multiply out the right side to get:<BR>\n" );
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document.write( "9 - 3 = 6<BR>\n" );
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document.write( "This simplifies to 6 = 6 which tells us that a = 3 is a good answer.<BR>\n" );
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document.write( "Next check a = -1 by substituting -1 for a in the original problem to get:<BR>\n" );
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document.write( "(-1)^2 - 3 = 2*(-1)<BR>\n" );
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document.write( "This reduces to:<BR>\n" );
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document.write( "1 - 3 = -2<BR>\n" );
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document.write( "-2 = -2 <BR>\n" );
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document.write( "So this answer for a checks also. Both our answers [a = 3 and a = -1] are correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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