Question

How do you solve \[100{x^2} = 121\] ?

Answer 1

Hint: Here in the above equation we can see the variable \[x\] and it is a quadratic equation. We are asked to solve the equation and find the value of \[x\] . It means that we need to find the value of \[x\] in such a way that it satisfies the given equation when its value is substituted in it. By applying some mathematical operations we can get the desired result.
Formula: In the above question we will simplify the equation by making variables on one side and numbers on the other and by square root we will simplify and find the value of \[x\]

Complete step by step solution:
Here we are asked to solve \[100{x^2} = 121\]
Now we will make \[{x^2}\] the subject and the equation becomes
 \[{x^2} = \dfrac{{121}}{{100}}\]
Now we will find the square root
 \[x = \pm \sqrt {\dfrac{{121}}{{100}}} \]
After simplification we will get
 \[x = + \dfrac{{11}}{{10}}\] Or \[x = - \dfrac{{11}}{{10}}\]
So the value of x comes out to be \[x = + \dfrac{{11}}{{10}}\] or \[x = - \dfrac{{11}}{{10}}\]
So, the correct answer is “ \[x = + \dfrac{{11}}{{10}}\] or \[x = - \dfrac{{11}}{{10}}\] ”.

Note: The basic rule to solve the quadratic equation \[({x^2})\] is to make it equal to \[0\] . However for the above equation there is exception because there is no term in \[x\]
There are various ways to solve the above question. We can also solve the question through alternate method
 \[100{x^2} - 121 = 0\]
Now we will factorize and get
 \[(10x + 11)(10x - 11) = 0\]
Later on after simplification we get \[x = + \dfrac{{11}}{{10}}\] Or \[x = - \dfrac{{11}}{{10}}\]
We should be careful while calculating and keep in mind that the number of solutions to the given equation in one variable is always less than or equal to the degree of the polynomial in the equation provided.