What are all solutions to the equation x squared equals 81?

To determine all solutions to the equation ( x^2 = 81 ), we start by recalling that squaring a number yields a positive result. To find ( x ), we can take the square root of both sides of the equation.

When we take the square root of 81, we find two potential values for ( x ), since both 9 and -9 satisfy the equation ( x^2 = 81 ). This is because:

• If ( x = 9 ), then ( 9^2 = 81 ).

• If ( x = -9 ), then ( (-9)^2 = 81 ).

Thus, the complete set of solutions that satisfy the equation ( x^2 = 81 ) includes both 9 and -9. It’s essential to note that the square root operation yields both a positive and a negative solution when dealing with equations of this form.

Therefore, the correct answer encompasses both solutions: 9 and -9, which is represented accurately by the choice stating that both values are included.