Final answer:
After taking the square root of both sides of the equation and adding 4 to isolate x, the solution is determined to be approximately 11.07 or -3.07. However, these answers don't match the provided options.
Step-by-step explanation:
To solve the equation 2(x-4)² = 100 for x, first, divide both sides of the equation by 2 to isolate the squared term:
(x-4)² = 50
Now take the square root of both sides, keeping in mind there will be two solutions since a square root can be positive or negative:
x-4 = ±50
Adding 4 to both sides gives us the two possible solutions for x:
x = 4 + √50 or x = 4 - √50
√50 is approximately 7.07, so:
x ≈ 4 + 7.07 or x ≈ 4 - 7.07
Thus, the solutions are:
x ≈ 11.07 or x ≈ -3.07
However, none of the solutions given in the question (a, b, c, d) match these results. It is possible that there may have been a typo in the provided options, and it should be checked for accuracy.