Answer:
[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]
Step-by-step explanation:
We want to solve for x in the equation;
[tex](x-2)^2-18=0[/tex]
Add 18 to both sides
[tex](x-2)^2=18[/tex]
We solve by the square root method.
[tex]x-2=\pm \sqrt{18}[/tex]
[tex]x-2=\pm 3\sqrt{2}[/tex]
Add 2 to both sides
[tex]x=2\pm 3\sqrt{2}[/tex]
Split the plus or minus sign.
[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]
Therefore the exact solution is [tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]
