document.write( "Question 167165: Find a value for k that will make 4x^2 + 6.4 x + k a perfect square. Describe the procedure that you used which requires algebra \n" ); document.write( "
Algebra.Com's Answer #123118 by ptaylor(2198)\"\" \"About 
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\n" ); document.write( "4x^2 + 6.4 x + k-------------------------------------eq1
\n" ); document.write( "Let's first assume that the solution is the following and then solve for b:
\n" ); document.write( "(2x+b)^2 expand using FOIL;
\n" ); document.write( "4x^2+2bx+2bx+b^2=
\n" ); document.write( "4x^2+4bx+b^2--------------------Now this equation has to be identical to eq1 in all respects, so:
\n" ); document.write( "4b=6.4;
\n" ); document.write( "b=6.4/4=3.2/2----eq2
\n" ); document.write( "and
\n" ); document.write( "b^2=k----------eq3
\n" ); document.write( "substitute eq2 into eq3\r
\n" ); document.write( "\n" ); document.write( "(3.2/2)^2=k or
\n" ); document.write( "k=(3.2/2)^2 \r
\n" ); document.write( "\n" ); document.write( "substitute k=(3.2/2)^2 into eq1
\n" ); document.write( "4x^2+6.4x+(3.2/2)^2=(2x+3.2/2)^2\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "(2x+3.2/2)^2=4x^2 +(6.4/2)x +(6.4/2)x +(3.2/2)^2=
\n" ); document.write( "4x^2+6.4x+(3.2/2)^2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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