document.write( "Question 936933: Pls do help : $\"if+25+%2A+14+=374++find+the+number+base+used\"$ \n" ); document.write( "

Algebra.Com's Answer #570381 by rothauserc(4718) $\"\"$ $\"About$

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let x be our number base, then
\n" ); document.write( "25 = 2x+5
\n" ); document.write( "14 = x+4
\n" ); document.write( "374 = 3(x^2)+7x+4, therefore
\n" ); document.write( "(2x+5)*(x+4) = 3(x^2)+7x+4
\n" ); document.write( "2x^2 + 13x + 20 = 3x^2 +7x + 4
\n" ); document.write( "x^2 -6x -16 = 0
\n" ); document.write( "factor polynomial
\n" ); document.write( "(x-8)*(x+2) = 0
\n" ); document.write( "x = 8 or -2
\n" ); document.write( "either base will work, however, we mostly use positive bases.
\n" ); document.write( "in your problem
\n" ); document.write( "25 base 8 is 21
\n" ); document.write( "25 base -2 is 2*(-2) + 5 = 1
\n" ); document.write( "14 base 8 is 12
\n" ); document.write( "14 base -2 is 2
\n" ); document.write( "374 base 8 = 3*64 + 56 + 4 = 252
\n" ); document.write( "374 base -2 = 3*(4) + 7(-2) +4 = 2
\n" ); document.write( "1) for base 8 we have
\n" ); document.write( "21*12 = 252
\n" ); document.write( "252 = 252
\n" ); document.write( "2) for base -2 we have
\n" ); document.write( "2 *1 = 2
\n" ); document.write( "2 = 2
\n" ); document.write( "our answers check \r
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