We have to solve the equation with the square root method:
[tex]\begin{gathered} 2(x-4)^2-6=18 \\ 2(x-4)^2=18+6 \\ 2(x-4)^2=24 \\ (x-4)^2=\frac{24}{2} \\ (x-4)^2=12 \\ \sqrt[]{(x-4)^2}=\sqrt[]{12} \\ x-4=\pm\sqrt[]{12} \\ x=4\pm\sqrt[]{12} \\ x=4\pm2\sqrt[]{3} \end{gathered}[/tex]
Answer: The solutions are:
[tex]\begin{gathered} x_1=4-2\sqrt[]{3} \\ x_2=4+2\sqrt[]{3} \end{gathered}[/tex]
