Question

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

Answer 1

Answer:

$x_1 = 9$ and $x_2 = 11$.

Step-by-step 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:

• $x_1 = 9$,
• $x_2 = 11$.