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9x^2+30x+25=11
\n" ); document.write( "9x^2+30x+25-11=0
\n" ); document.write( "9x^2+30x+14=0 ----(1)
\n" ); document.write( "Given ax^2 +bx +c = 0, by formula x = [(-b)+ orminus sqrt(b^2-4ac)]/2a
\n" ); document.write( "Here a=9, b=30 and c-14
\n" ); document.write( "x= [(-30)+or minus sqrt(30^2-4X9X14)]/(2X9)
\n" ); document.write( "= [(-30)+or minus sqrt(900-504)]/(18)
\n" ); document.write( "= [(-30)+or minus sqrt(396)]/(18)
\n" ); document.write( "= [(-30)+or minus sqrt(36X11)]/(18)
\n" ); document.write( "= [(-30)+or minus 6sqrt(11)]/(18)
\n" ); document.write( "= [-5+orminus rt(11)]/3 (cancelling 6 in the nr and in the dr)
\n" ); document.write( "Therefore
\n" ); document.write( "x= (-5+sqrt(11)]/3 or x= (-5-sqrt(11)]/3
\n" ); document.write( "Verification: Putting x=(-5+sqrt(11)]/3 in (1)
\n" ); document.write( "LHS = 9x^2+30x+14
\n" ); document.write( "= [-5+rt(11)]^2+10[-5+rt(11)]+14
\n" ); document.write( "=(-5)^2+ (rt(11))^2-10rt(11)-50+10rt(11)+14
\n" ); document.write( "=25+11-50+14
\n" ); document.write( "=50-50=0
\n" ); document.write( "=RHS
\n" ); document.write( "Note: Since quadratic surds occur in conjuagate pairs
\n" ); document.write( "the other value also must hold\r
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