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

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

• A. 9
• B. -9
• C. 9 and -9
• D. 10

Answer: (C)

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.

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.