The root method requires us to leave the expression that is raised to the power of 2 on one side of the equality. We do so, by applying mathematical operations on both sides of the equation
We begin with the equation
[tex]2(x-4)^{2}-6=18[/tex]
First, we add 6 on both sides, so we get
[tex]2(x-4)^{2}=18+6=24[/tex]
Then, we divide boths sides by 2, so we get
[tex](x-4)^{2}=\frac{24}{2}=12[/tex]
Now, we take the square root on both sides. Have in mind that once we take the square root we should consider the positive and negative root. So we get
[tex]x-4=\pm\sqrt[]{12}[/tex]
Finally, we add 4 on both sides, so we get
[tex]x=4\pm\sqrt[]{12}[/tex]
This is equivalent to have the solutions
[tex]x=4+\sqrt[]{12}[/tex]
and
[tex]x=4-\sqrt[]{12}[/tex]
