Solve the equation 𝑥 squared equals 16.
We can solve this equation using the balancing method and our knowledge of inverse operations. The opposite or inverse of squaring is square rooting. So, our first step is to square-root both sides of the equation. The square root of 𝑥 squared is equal to 𝑥. On the right-hand side, we have the square root of 16.
Remember that once we have square-rooted 16, we can have the positive or negative of this value. The square root of 16 is equal to four as four multiplied by four is 16. There are two possible solutions to the equation 𝑥 squared equals 16. They are 𝑥 equals four and 𝑥 equals negative four.
We can check these by substituting our values back in to the original equation. Four squared is equal to four multiplied by four. This is equal to 16. Therefore, our first solution is correct. Squaring negative four involves multiplying negative four by negative four. Multiplying two negative numbers gives a positive answer. Therefore, negative four squared is also 16.