Instructions: determine which step/s in the solution of the given problem the error/s (if any) occurred and give an explanation.


-problem: the difference of three times a number and two is the same as -9 times the square of the number. determine all such numbers.


solution:
step 1: let x be the number
3x-2=-9x²

step 2: 9x²+3x-2=0

step 3: 9x²-6x+3x-2=0

step 4: (9x²-6x)+ (3x-2) =0
3x(3x-2)+(3x-2)=0

step 5: (3x-2)(3x+1)=0
3x-2=0. 3x+1=0

step 6: 3x=-2. 3x=1
x= -⅔ x= ⅓

final answer: The numbers are -⅔ and ⅓.


is there an error in the steps? if so explain.

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