Solve. x² – 81 = 0
A. 0
B. –9
C. –9, 9
D. 9
C. –9, 9
To solve the equation x² – 81 = 0, we can factor it.
We rewrite the equation as x² – 9² = 0.
Notice that this is a difference of squares because 9² = 81.
(x – 9)(x + 9) = 0.
To find the values of x that satisfy the equation, we set each factor equal to zero.
Setting x – 9 = 0, we solve for x:
x = 9.
Setting x + 9 = 0, we solve for x:
x = –9.
Therefore, the solutions to the equation x² – 81 = 0 are x = –9 and x = 9.
The correct answer is C. –9, 9.