Multiple choice

Solve the following quadratic equation by factorization method: $(2x+3)^2-81=0$

  1. ${-6, 3}$ 
  2. ${-6, 2}$ 
  3. ${-3, 3}$ 

  4. None of these
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A Correct answer
Explanation

(2x+3)^2 = 81. Taking square roots, 2x+3 = 9 or 2x+3 = -9. If 2x+3 = 9, 2x = 6, x = 3. If 2x+3 = -9, 2x = -12, x = -6.

AI explanation

We solve the equation (2x + 3)^2 - 81 = 0 by moving 81 to the other side to get (2x + 3)^2 = 81. Taking the square root of both sides yields two equations, 2x + 3 = 9 and 2x + 3 = -9. Solving the first equation gives x = 3, and solving the second equation gives x = -6. The solution set is {-6, 3}.

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