What is the solution for x in the equation -2,493 = -4(66 - x)^(4/2) + 7?

To solve the equation -2,493 = -4(66 - x)^(4/2) + 7, we start by simplifying the equation.

First, simplify the exponent. The term (66 - x)^(4/2) can be expressed as (66 - x)^2 since 4/2 equals 2. This rewrites the equation as:

-2,493 = -4(66 - x)^2 + 7.

Next, we subtract 7 from both sides to isolate the term involving x:

-2,493 - 7 = -4(66 - x)^2

-2,500 = -4(66 - x)^2.

Now, divide both sides by -4 to simplify further:

625 = (66 - x)^2.

At this point, we take the square root of both sides. Remember that the square root can yield both positive and negative values:

66 - x = ±25.

This gives us two equations to solve:

1. 66 - x = 25

2. 66 - x = -25.

For the first equation, solve for x:

66 - 25 = x

x = 41.

For the second equation, we can