What are all the solutions for x if 3x2 - 2x-21= 0?
Correct answer: E. x= 3 or x = -7/3
- A. x = -21 only
- B. x = -7 or x = 3
- C. x = -3 or x = 7/3
- D. x = -7/3 or x = -3
- E. x= 3 or x = -7/3
Explanation
Split the middle term into two terms: 3x²-9x+7x-21=0 Factor the first two terms and the last two terms separately: 3x(x-3)+7(x-3)=0 Factor out: (x-3) (3x+7)=0 Apply Zero Product Property: 2-3=0 or 3x+7=0 Rearrange unknown terms to the left side of the equation: 2 =3 Rearrange unknown terms to the left side of the equation: 3x =-7 Divide both sides of the equation by the coefficient of variable: =-7÷3 Rewrite as fraction: -3/7 Combine the results: x =3 or x=-7/3 Answer: x=3 or =- 7 /3
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