Final answer:
The solutions to x² = 7 are √7 and -√7 because both, when squared, equal 7. The options √-7, 49, and -49 do not satisfy the equation.
Step-by-step explanation:
To find the solutions to the equation x² = 7, we need to consider what number, when squared, equals 7. The solutions can be either positive or negative, since squaring either will result in a positive number. The square root of 7, √7, is a solution because (√7)² = 7. Also, the negative square root, -√7, is a solution because (-√7)² also equals 7. The other options, √-7, 49, and -49, do not satisfy the equation when squared. Thus, the correct solutions are √7 and -√7.
To verify solutions to a quadratic equation, such as x² = 7, we check if the solutions make the original equation true. In this case, the only numbers that do so when squared are √7 and -√7.