Question

How do you solve the equation $ 3{(x - 2)^2} - 12 = 0 $ ?

Answer 1

Hint: Take the given expression and solve it by using square and square root concepts. Also, use the basic mathematical expressions and concepts to simplify and get the required resultant value for the unknown term “x”

Complete step-by-step solution:
Take the given expression: $ 3{(x - 2)^2} - 12 = 0 $
Take common multiples from both the terms in the above expression.
 $ 3[{(x - 2)^2} - 4] = 0 $
Move constant on the opposite side. Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow [{(x - 2)^2} - 4] = \dfrac{0}{3} $
Zero upon any number is always zero.
 $ \Rightarrow [{(x - 2)^2} - 4] = 0 $
Now move the term on the right hand side of the equation. When you move any term from one side to another then the sign of the term changes. Positive term changes to negative and vice versa.
 $ \Rightarrow {(x - 2)^2} = 4 $
The above can be re-written as: \[{(x - 2)^2} = {2^2}\]
Take the square root on both the sides of the above equation.
 $ \Rightarrow \sqrt {{{(x - 2)}^2}} = \sqrt {{2^2}} $
Square and square root cancel each other on both the sides of the above equation.
 $ \Rightarrow x - 2 = 2 $
Make required “x” the subject and move other terms on the opposite side. When you move any term from one side to another then the sign of the term changes. Positive term changes to negative and vice versa.
 $ \Rightarrow x = + 2 + 2 $
Simplify the above equation-
 $ \Rightarrow x = 4 $
This is the required solution.

Note: Be good in numbers and remember the square and square root till twenty at least for an efficient and accurate solution. Be careful about the sign convention when you move any term from one side to another, and the change of sign according to its original sign.