Answer: The correct option is (B) \((x-3)^2=23.\)
Step-by-step explanation: We are given to complete the square and transform the following quadratic equation in the form \((x-p)^2=q.\)
\(x^2-6x-8=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We have
\(x^2-6x-8=6\\\\\Rightarrow x^2-6x=6+8\\\\\Rightarrow x^2-6x=14\\\\\Rightarrow x^2-2\times x\times 3+3^2=14+3^2\\\\\Rightarrow (x-3)^2=14+9\\\\\Rightarrow (x-3)^2=23.\)
Thus, the required transformed form of given equation (i) is
\((x-3)^2=23,\)
where p = 3 and q = 23.
Option (B) is CORRECT.
