Question

How do you solve $ 3{x^2} = 12 $ ?

Answer 1

Hint: Here we will use the concept of basic mathematics in simplification and we use the concepts of square and square root as the given term is the form of square of the variable equivalent to the constant.

Complete step-by-step answer:
Take the given expression-
 $ 3{x^2} = 12 $
When the term multiplicative on one side is moved to the opposite side, then it goes to the denominator.
 $ \Rightarrow {x^2} = \dfrac{{12}}{3} $
Find out the factors on the right hand side of the equation.
 $ \Rightarrow {x^2} = \dfrac{{4 \times 3}}{3} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
 $ \Rightarrow {x^2} = 4 $
Take square-root on both the sides of the equation.
 $ \Rightarrow \sqrt {{x^2}} = \sqrt 4 $
Square and square-root cancel each other on the left hand side of the equation.
 $ \Rightarrow x = \sqrt 4 $
Square of the negative or the positive terms always gives positive terms.
 $ \Rightarrow x = 2 $ or $ \Rightarrow x = ( - 2) $
So, the correct answer is “x = 2 OR x = -2”.

Note: Know the concepts of squares and square-root. Square is the number multiplied itself and cube it the number multiplied thrice. Square is the product of same number twice such as $ {n^2} = n \times n $ for Example square of $ 2 $ is $ {2^2} = 2 \times 2 $ simplified form of squared number is $ {2^2} = 2 \times 2 = 4 $ and square-root is denoted by $ \sqrt {{n^2}} = \sqrt {n \times n} $ For Example: $ \sqrt {{2^2}} = \sqrt 4 = 2 $