document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201065>Question 201065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of a and b that result in the given sum.\r<BR>\n" );
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document.write( "[(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2 - 4x + 7\r<BR>\n" );
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document.write( "Please help. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151303 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=151303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [(a+1)x^2 + bx + 2] + [(b-2)x^2 - ax + 5] = x^2 - 4x + 7 ... Start with the given equation.\r<BR>\n" );
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document.write( "(a+1)x^2 + bx + 2 + (b-2)x^2 - ax + 5 = x^2 - 4x + 7 ... Remove the brackets\r<BR>\n" );
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document.write( "[(a+1)x^2+ (b-2)x^2] + [ bx - ax] + [2  + 5] = x^2 - 4x + 7 ... Group like terms.\r<BR>\n" );
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document.write( "(a+1+b-2)x^2 + (b-a)x + 7 = x^2 - 4x + 7 ... Combine like terms.\r<BR>\n" );
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document.write( "(a+b-1)x^2 + (b-a)x + 7 = x^2 - 4x + 7 ... Simplify\r<BR>\n" );
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document.write( "Now just equate the coefficients to get the two equations:\r<BR>\n" );
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document.write( "a+b-1=1<BR>\n" );
document.write( "b-a=-4\r<BR>\n" );
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document.write( "So simply solve this system (which I'll let you do) using any method to get the answers\r<BR>\n" );
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document.write( "a=3, b=-1\r<BR>\n" );
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