Question

How do you solve $\sqrt {x + 9} = 4$ ?

Answer 1

Hint: We are given with a simple equation and asked to solve for $x$. We need to rearrange or alter the given equation. For that first, we have to separate the variables from the numbers by transferring it to the other side. Then, we have to solve the given problem by using the basic mathematical operations and transferring methods for solving the given equations.

Complete step-by-step solution:
The given equation is $\sqrt {x + 9} = 4$ and we need to solve for $x$ .
This is a simple equation, we can solve by using the transferring method.
We need to separate the variable and the numbers.
First, we will take square on both sides to eliminate the square root in the left hand side,
$ \Rightarrow \sqrt {x + 9} = 4$
Taking square on both sides,
$ \Rightarrow x + 9 = {4^2}$
And it becomes,
$ \Rightarrow x + 9 = 16$
Transferring $9$ to the other side, it will become $ - 20$,
$ \Rightarrow x = 16 - 9$
Now, we have to subtract $9$ from $16$ to find the value of $x$,
$ \Rightarrow x = 7$

Therefore the value of $x$ is $7$.

Note: After getting the answer, always apply the value of the variable in the given equation to check it whether the answer obtained is correct or not.
If this type of questions are asked in MCQ type, you can save your time by directly applying the given choices in the place of $x$ and check whether the equation satisfies them.
For example, assume that for this question they have given choices like,
Find $x$ , $x + 9 = 16$.
$a)3{\text{ b)2 c)7}}$
You can directly substitute the values in $x + 9 = 16$ and check,
If $x = 3$ the equation is not satisfied
If $x = 2$ the equation is not satisfied
If $x = 7$ the equation gets satisfied.
Therefore $7$ is the correct answer.