Question

How do you solve `(x - 8)^2 = 48`?

Answer 1

See a solution process below:

Explanation:

First, take the square root of each side of the equation to eliminate the exponent while keeping the equation balanced. Remember, the square root of a number gives both a positive and a negative result:

`sqrt((x - 8)^2) = +-sqrt(48)`

`x - 8 = +sqrt(48)` and `x - 8 = -sqrt(48)`

`x - 8 = sqrt(16 * 3)` and `x - 8 = -sqrt(16 * 3)`

`x - 8 = sqrt(16) * sqrt(3)` and `x - 8 = -sqrt(16)sqrt(3)`

`x - 8 = 4sqrt(3)` and `x - 8 = -4sqrt(3)`

`x - 8 + color(red)(8) = 4sqrt(3) + color(red)(8)` and `x - 8 + color(red)(8) = -4sqrt(3) + color(red)(8)`

`x - 0 = 4sqrt(3) + 8` and `x - 0 = -4sqrt(3) + 8`

`x = 4sqrt(3) + 8` and `x = -4sqrt(3) + 8`