Answer:
[tex]x_1 = 9[/tex] and [tex]x_2 = 11[/tex].
Step-by-step explanation:
Start by adding 1 to both sides of this equation.
[tex](x - 10)^{2} = 1[/tex].
The square of what number or numbers will lead to the number "1"? It turns out that not only [tex]1^{2} = 1[/tex], but [tex](-1)^{2}= 1[/tex] as well. In other words, the value [tex](x - 10)[/tex] 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 [tex]x - 10 = 1[/tex]. Add 10 to both sides of the equation. [tex]x = 11[/tex].
Now, consider the case when [tex]x - 10 = -1[/tex]. Again, add 10 to both sides of the equation, [tex]x = 9[/tex].
Order the two solutions in an increasing order:
