Solve the given quadratic equation using the square root property. $2x^2-16=0$

• A. $x=0,x=-2$
• B. $x=4\sqrt2,x=-4\sqrt2$
• C. $x=4,x=-4$
• D. $x=2\sqrt2,x=-2\sqrt2$

Answer: (D)

Verified step by step guidance

1. Start by isolating the quadratic term. The given equation is 2x^2 - 16 = 0. Add 16 to both sides to get 2x^2 = 16.
2. Divide both sides of the equation by 2 to solve for x^2. This gives x^2 = 8.
3. Apply the square root property to solve for x. The square root property states that if x^2 = a, then x = ±√a. Therefore, x = ±√8.
4. Simplify the square root of 8. Note that √8 can be expressed as √(4 * 2), which simplifies to 2√2.
5. Conclude that the solutions to the equation are x = 2√2 and x = -2√2.