Question

Solve for x. Write the smaller solution first, and the larger solution second. (x-10)^2-1=0

Answer 1

`x_1 = 9` and
`x_2 = 11`.

Explanation:

Start by adding 1 to both sides of this equation.

`(x - 10)^(2) = 1`.

The square of what number or numbers will lead to the number "1"? It turns out that not only
`1^(2) = 1`, but
`(-1)^(2)= 1` as well. In other words, the value
`(x - 10)` can be either 1 or -1. Either way, the equation is still going to hold. That's the reason why there are two solutions to this equation.

Consider the case when
`x - 10 = 1`. Add 10 to both sides of the equation.
`x = 11`.

Now, consider the case when
`x - 10 = -1`. Again, add 10 to both sides of the equation,
`x = 9`.

Order the two solutions in an increasing order:

• 
  `x_1 = 9`,
• 
  `x_2 = 11`.