Multiple choice

Solve the following quadratic equations by factorization method: $3(x-4)^2-5(x-4)=12$

  1. $\left \{ 7, \dfrac{8}{3} \right \}$ 
  2. $\left \{ -7, \dfrac{8}{3} \right \}$ 
  3. $\left \{ 7, \dfrac{-8}{3} \right \}$ 

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u = x-4. The equation is 3u^2 - 5u - 12 = 0. Factoring gives (3u + 4)(u - 3) = 0, so u = -4/3 or u = 3. If x-4 = -4/3, x = 8/3. If x-4 = 3, x = 7.

AI explanation

Assume y = x - 4 to rewrite the equation as 3(y)^2 - 5y = 12, which simplifies to 3y^2 - 5y - 12 = 0. Factoring the quadratic yields (3y + 4)(y - 3) = 0, giving y = -4/3 or y = 3. Substituting back x - 4 for y gives x - 4 = -4/3 or x - 4 = 3, resulting in x = 8/3 or x = 7. The solution set is 7, 8/3.

Keep practicing — related questions