Question

How do you solve $2{{x}^{2}}=242$ ?

Answer 1

Hint: In this question, we have to find the value of x. Thus, we will apply the algebraic identity to get the solution. We start solving this problem by dividing 2 on both sides in the above equation and then we will subtract 121 on both sides. After the necessary calculations, we will apply the algebraic identity $(a+b)(a-b)={{a}^{2}}-{{b}^{2}}$ on the left-hand side of the equation. Thus, we get two equations and solve them separately, to get the required result for the solution.

Complete step by step solution:
According to the question, we have to find the value of x.
Thus, we will apply the basic mathematical rules and the algebraic identity to get the solution.
The equation given to us is $2{{x}^{2}}=242$ ---------- (1)
First, we will divide 2 on both sides in equation (1), we get
$\Rightarrow \dfrac{2}{2}{{x}^{2}}=\dfrac{242}{2}$
On further simplification, we get
$\Rightarrow {{x}^{2}}=121$
Now, we will subtract 121 on both sides in the above equation, we get
$\Rightarrow {{x}^{2}}-121=121-121$
As we know, the same terms with opposite signs cancel out each other, therefore we get
$\Rightarrow {{x}^{2}}-121=0$
Now, we will apply the algebraic identity $(a+b)(a-b)={{a}^{2}}-{{b}^{2}}$ on the left-hand side in the above equation, we get
$\Rightarrow (x-11)(x+11)=0$
Thus, we get two new separate equations, that is
$\Rightarrow x-11=0$ and --------- (2)
$\Rightarrow x+11=0$ ------ (3)
Now, we will first solve equation (2), which is
$\Rightarrow x-11=0$
So, we will add 11 on both sides in the above equation, we get
$\Rightarrow x-11+11=0+11$
As we know, the same terms with opposite signs cancel out each other, therefore we get
$\Rightarrow x=11$
Now, we will first solve equation (3), which is
$\Rightarrow x+11=0$
So, we will subtract 11 on both sides in the above equation, we get
$\Rightarrow x+11-11=0-11$
As we know, the same terms with opposite signs cancel out each other, therefore we get
$\Rightarrow x=-11$

Therefore, for the equation $2{{x}^{2}}=242$, the value of x is equal to 11, -11.

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical errors. One of the alternative methods to solve this problem is first to subtract 242 and then divide 2 on both sides in the equation. Then, we will apply the algebraic identity and make the necessary changes to get the solution.