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Solve: ${x^2} - \left( {3\sqrt 2 + 2i} \right)x + 6i\sqrt 2 = 0$

Answer
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Hint: - Factorize the quadratic equation
Given equation is
$
  {x^2} - \left( {3\sqrt 2 + 2i} \right)x + 6i\sqrt 2 = 0 \\
   \Rightarrow {x^2} - 3\sqrt 2 x - 2ix + 6i\sqrt 2 = 0 \\
   \Rightarrow x\left( {x - 3\sqrt 2 } \right) - 2i\left( {x - 3\sqrt 2 } \right) = 0 \\
   \Rightarrow \left( {x - 3\sqrt 2 } \right)\left( {x - 2i} \right) = 0 \\
   \Rightarrow \left( {x - 3\sqrt 2 } \right) = 0,{\text{ }}\left( {x - 2i} \right) = 0 \\
   \Rightarrow x = 3\sqrt 2 {\text{ and }}x = 2i \\
$
So, this is the required solution of the given equation.

Note: - In such types of questions the key concept is that we have to factorize the given equation, then we will get the required answer.