document.write( "Question 1146571: the tens digits of a certain number is 7 less than the units digit .the sum of the squares of the two digits is 85.find the number.with justification \n" ); document.write( "
Algebra.Com's Answer #767853 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
t = the tens digit
\n" ); document.write( "u = the units
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement
\n" ); document.write( ":
\n" ); document.write( "the tens digits of a certain number is 7 less than the units digit.
\n" ); document.write( "t = u - 7
\n" ); document.write( "the sum of the squares of the two digits is 85.
\n" ); document.write( "t^2 + u^2 = 85
\n" ); document.write( "replace t with (u-7)
\n" ); document.write( "(u-7)^2 + u^2 = 85
\n" ); document.write( "FOIL(u-7)(u-7)
\n" ); document.write( "u^2 - 14u + 49 + u^2 - 85 = 0
\n" ); document.write( "2u^2 - 14u - 36 = 0
\n" ); document.write( "simplify divide 2
\n" ); document.write( "u^2 - 7u - 18 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(u-9)(u+2) = 0
\n" ); document.write( "the positive solutin
\n" ); document.write( "u = 9
\n" ); document.write( "then
\n" ); document.write( "t = 9 - 7
\n" ); document.write( "t = 2
\n" ); document.write( "find the number.with justification
\n" ); document.write( "Number is 29
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check: 2^2 + 9^2 = 81 + 4 = 85 \n" ); document.write( "
\n" );