Question

How do you solve${x^2} - 20 = 0$?

Answer 1

Hint: In this question, we are given with an equation and are asked to solve it. This is a simple equation, we are able to find the value of $x$ by transferring all the other terms to the opposite side and equate it. On doing some simplification we get the required answer.

Complete step by step answer:
The given equation is ${x^2} - 20 = 0$and we need to solve for $x$ .
This is a simple equation, we can solve by using the transferring method.
First we need to separate the variable and the numbers.
$ \Rightarrow {x^2} - 20 = 0$
Transferring $ - 20$ to the other side, it will become$ + 20$ . Clearly adding zero and $ + 20$ we get,
$ \Rightarrow {x^2} = 20$
Now, since the variable is in square, we have to transfer it to the other side and it becomes the square root,
$ \Rightarrow x = \pm \sqrt {20} $
Now, in order to find the value of the square root of $20$ easily, we will split the number into its factors.
Splitting $20$ as $2 \times 10$
$ \Rightarrow x = \pm \sqrt {2 \times 10} $
Now, we can split $10$ into its factors, i.e. $2 \times 5$
$ \Rightarrow x = \pm \sqrt {2 \times 2 \times 5} $
As we can see, there are two $2$, we can take any pair out of this square root as we need only those numbers which are in pairs to take it out.
$ \Rightarrow x = \pm 2\sqrt 5 $

Therefore the value of $x$ is $ \pm 2\sqrt 5 $

Note: Alternative method:
If students are confused about the signs and operations when transferring the number to the other sides, they can follow this.
Given question is ${x^2} - 20 = 0$
To eliminate the number in the left hand side, we have to rearrange or add or subtract the same number so that it will become$0$.
Keep in mind that, whatever you do, you have to do it on both the sides.
Now, adding $20$ on both the sides,
$ \Rightarrow {x^2} - 20 + 20 = 0 + 20$
And it becomes,
$ \Rightarrow {x^2} = 20$
Now in order to cancel the square in the variables, we will take square roots on both sides.
Taking square roots on both sides,
$ \Rightarrow \sqrt {{x^2}} = \sqrt {20} $
And it becomes,
$ \Rightarrow x = \pm \sqrt {20} $
Therefore we get the answer $x = \pm 2\sqrt 5 $.