If x^2 - 9 = 0, what are the solutions for x?

If x^2 - 9 = 0, what are the solutions for x?

• A. x = 3
• B. x = -3
• C. x = 3 or x = -3
• D. x = 0

Answer: (C)

The equation is a difference of squares, so it factors nicely: x^2 - 9 = (x - 3)(x + 3). When a product is zero, at least one factor must be zero. Setting each factor to zero gives x = 3 or x = -3. Both values satisfy the original equation, since 3^2 - 9 = 0 and (-3)^2 - 9 = 0. The value x = 0 doesn’t work because 0^2 - 9 = -9, not 0. So the solutions are x = 3 or x = -3.

The equation is a difference of squares, so it factors nicely: x^2 - 9 = (x - 3)(x + 3). When a product is zero, at least one factor must be zero. Setting each factor to zero gives x = 3 or x = -3. Both values satisfy the original equation, since 3^2 - 9 = 0 and (-3)^2 - 9 = 0. The value x = 0 doesn’t work because 0^2 - 9 = -9, not 0. So the solutions are x = 3 or x = -3.