Step-by-step explanation:
[tex](x - 2) {}^{2} - 41 = 8[/tex]
Solve for x by taking the square root of both sides.
[tex](x - 2 )- 41 = 2\sqrt{2} [/tex]
Use two serpate equations because a square root is positive and negative
[tex](x - 2) - 41 = - 2 \sqrt{2} [/tex]
Add 41 on both sides
[tex]x - 2 = 2 \sqrt{2} + 41[/tex]
[tex]x - 2 = - 2 \sqrt{2} + 41[/tex]
Isolate x.
[tex]x = 2 \sqrt{2} + 43[/tex]
[tex]x = - 2 \sqrt{2} + 43[/tex]
