#A

     ,=MULA = ,QUADRATIC ,EQUA;N
  ,! SOLU;NS ( ! EQUA;N ;;;AX9#B"6BX
"6C "7 #J;' >E
    X "7 ("-B_6%B9#B"-#D;AC+./#B;A)
,? =MULA %D 2 MEMORIS$4 ,! EXPRES.N
"<AX;9#B"6BX"6C"> MAY 2 MADE EQUAL TO
ANY GIV5 QUADRATIC EXPRES.N1 BY GIV+
A1 ;B & ;C SUITABLE VALUES4 ,TO MAKE
"<AX;9#B"6BX"6C"> EQUAL TO "<#EX;9#B
"-#BX"6#F">1 = EXAMPLE1 PUT A "7 #E1
;B "7 "-#B1 & ;C "7 "-#F4
  ,! =MULA MAY 2 PROV$ BY ! ME?OD (
COMPLET+ ! SQU>E1 APPLI$ TO ! EQUA;N
;;;AX9#B"6BX"6C "7 #J;'4
  ,RE>RANGE3
    AX9#B"6BX "7 "-C4
,DIVIDE "? BY A3
    X9#B"6(B./A)X "7 "-(C./A)4
,ADD TO EA* SIDE ;;;"<#A/B COEFFICIENT
OF X">9#B;'3
    X9#B"6(B./A)X"6"<(B./#B;A)">9#B
      "7 "-(C./A)"6(B9#B./#D;A9#B)
OR
                                    #B
    "<X"6(B./#B;A)">9#B "7
      (B9#B"-#D;AC./#B;A9#B)4
,TAKE ! SQU>E ROOT ( BO? SIDES3
    X"6(B./#B;A) "7 _6(%B9#B"-#D;AC+./
      #B;A)4
,SUBTRACT ;(B./#B;A) F EA* SIDE3
    X "7 "-(B./#B;A)_6(%B9#B"-#D;AC+./
      #B;A)
OR
    X "7 ("-B_6%B9#B"-#D;AC+./#B;A)4