Answer: The correct option is (D) \(x=-2\pm\sqrt5.\)
Step-by-step explanation: We are given to solve the following quadratic equation :
\(3x^2+12x=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the method of COMPLETING THE SQUARE to solve the given problem where the following square formula is used :
\(a^2+2ab+b^2=(a+b)^2.\)
From equation (i), we have
\(3x^2+12x=3\\\\\Rightarrow 3(x^2+4x)=3\\\\\Rightarrow x^2+4x=1\\\\\Rightarrow x^2+2\times x\times2+2^2=1+2^2\\\\\Rightarrow (x+2)^2=1+4\\\\\Rightarrow (x+2)^2=5\\\\\Rightarrow x+2=\pm\sqrt5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=-2\pm\sqrt5.\)
Thus, the required solution of the given quadratic equation is
\(x=-2\pm\sqrt5.\)
Option (D) is CORRECT.
