18. \( \sqrt{-x+1}-6=0 \)

To solve the equation \( \sqrt{-x+1}-6=0 \), first isolate the square root on one side: \[ \sqrt{-x+1} = 6 \] Next, square both sides to eliminate the square root: \[ -x + 1 = 36 \] Now, solve for \( x \): \[ -x = 36 - 1 \] \[ -x = 35 \] \[ x = -35 \] Finally, always check your answer by substituting it back into the original equation: \[ \sqrt{-(-35)+1}-6 = \sqrt{35+1}-6 = \sqrt{36}-6 = 6-6 = 0 \] Thus, the solution to the equation is \( x = -35 \).