Multiple choice

Solve the equation by the zero-factor property $2{ x }^{ 2 }=18x-36$

  1. $\left\{ -6,3 \right\} $
  2. $\left\{ -6,-3 \right\} $
  3. $\left\{ 3,6 \right\} $
  4. $\left\{ 6,12 \right\} $
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C Correct answer
Explanation

2x^2 - 18x + 36 = 0. Divide by 2: x^2 - 9x + 18 = 0. Factor: (x-3)(x-6) = 0. Roots are 3 and 6.

AI explanation

Rearrange the given equation into standard form by subtracting 18x and adding 36 to both sides to get 2x^2 - 18x + 36 = 0. Divide the entire equation by 2 to simplify it to x^2 - 9x + 18 = 0. Using the zero-factor property, we factor the quadratic to get (x - 3)(x - 6) = 0, which gives the roots as 3 and 6. The solution set is {3, 6}.

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