To solve the radical equation \( 12 + \sqrt{x^4 - 10} = 8 \), the first step you should take is to subtract 12 from both sides of the equation.
This simplifies the equation to: \[ \sqrt{x^4 - 10} = 8 - 12 \] \[ \sqrt{x^4 - 10} = -4 \] Since the square root cannot equal a negative number, this leads to no solutions.
So, the correct first step is: Subtract 12 from both sides of the equation.