Final answer:
The equation x² = 81 is solved by taking the square root of 81, which is 9. Since both positive and negative numbers squared give a positive result, the solutions are x = 9 and x = -9.
Step-by-step explanation:
To solve the equation x² = 81, we look for a number that, when squared, equals 81. This can be achieved through simple square roots. The steps to solve this equation are as follows:
- Recognize that the equation is asking for the square root of 81, since x² means x times x, and we want to find what x is when squared to get 81.
- Calculate the square root of 81. The square root of 81 is 9 because 9 squared (9 x 9) is 81.
- However, we have to consider both the positive and negative roots because squaring either positive or negative 9 will result in 81. So, there are two solutions: x = 9 and x = -9.
Therefore, the equation x² = 81 has two solutions: x = 9 and x = -9. No need for more complicated methods such as the quadratic formula since this is a simple square root problem.