Solve 𝑥 plus six all squared equals four.
In order to solve this question, we will use the balancing method and our knowledge of inverse operations. The inverse or opposite of squaring is square rooting, so we begin by square rooting both sides. The left-hand side becomes 𝑥 plus six. The right-hand side becomes the square root of four. We recall that after square rooting, we can take the positive or negative of that answer.
As the square root of four is equal to two, we have 𝑥 plus six is equal to positive or negative two. This means that we will have two possible solutions, 𝑥 plus six equals two or 𝑥 plus six is equal to negative two. In both of these situations, we need to subtract six from both sides of the equation as subtracting is the opposite of adding. Two minus six is equal to negative four. And negative two minus six is equal to negative eight. There are two solutions to the equation 𝑥 plus six all squared equals four. They are 𝑥 equals negative four and 𝑥 equals negative eight.
We could check these answers by substituting our values back into the equation. For our first solution, we have negative four plus six all squared. Negative four plus six is equal to two, and squaring two does indeed give us four. Substituting in 𝑥 equals negative eight gives us negative eight plus six all squared. Negative eight plus six is equal to negative two. Squaring a negative number gives a positive answer. Therefore, our second solution is also correct.