Final answer:
To solve the equation |x^2-16|=0, isolate the absolute value expression, set equal to 0, and solve for x. There are two solutions: x=4 and x=-4.
Step-by-step explanation:
To solve the equation |x2-16|=0, we need to isolate the absolute value expression and set it equal to 0. Solving for x, we have two cases:
Case 1: x2-16=0. Adding 16 to both sides, we get x2=16. Taking the square root of both sides, we have x=±4. Therefore, the solutions are x=4 and x=-4.
Case 2: -(x2-16)=0. Distributing the negative sign, we have -x2+16=0. Rearranging, we get x2-16=0, which is the same as Case 1. So, the solutions are x=4 and x=-4.