Multiple choice

Solve the following quadratic equations by factorization method: $3(x^2-6)=x(x+7)-3$

  1. $\left \{ -\dfrac{3}{2}, 5 \right \}$ 
  2. $\left \{ \dfrac{3}{2}, 5 \right \}$ 
  3. $\left \{ -\dfrac{3}{2}, -5 \right \}$ 

  4. None of these
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A Correct answer
Explanation

Expanding both sides of the equation gives 3x^2 - 18 = x^2 + 7x - 3. Rearranging all terms to one side yields the quadratic equation 2x^2 - 7x - 15 = 0. Factoring this expression gives (2x + 3)(x - 5) = 0, which has the roots x = -3/2 and x = 5.

AI explanation

Simplify the equation 3(x^2 - 6) = x(x + 7) - 3 to get 3x^2 - 18 = x^2 + 7x - 3. Rearranging terms yields the quadratic equation 2x^2 - 7x - 15 = 0. By splitting the middle term, we factor it as 2x^2 - 10x + 3x - 15 = 0, giving (2x + 3)(x - 5) = 0. The roots are x = -3/2 and x = 5.

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