Question

How do you solve $ {(x + 2)^2} = 16 $ ?

Answer 1

Hint: Here first of we will take the given expression and apply the equivalent functions on both the sides of the equation and then will apply the concepts of square-root on both the sides of the equation and then will accordingly find the value for the variable “x”.

Complete step-by-step answer:
Take the given expression-
 $ {(x + 2)^2} = 16 $
The above equation can be re-written as –
 $ {(x + 2)^2} = {4^2} $
Take the square root on both sides of the equation.
 $ \Rightarrow \sqrt {{{(x + 2)}^2}} = \sqrt {{4^2}} $
Square and square-root cancel each other on both the sides of the equation.
 $ \Rightarrow x + 2 = 4 $
Take constants on one side of the equation. When you move any one side of the equation, the sign of the terms also changes. Positive terms become negative when moved from one side to another.
 $ \Rightarrow x = 4 - 2 $
Simplify the above equation –
 $ \Rightarrow x = 2 $
So, the correct answer is “x = 2 ”.

Note: Constants are the terms with fixed value such as the numbers it can be positive or negative whereas the variables are terms which are denoted by small alphabets such as x, y, z, a, b, etc. Be careful while moving any term from one side to another. Remember when you change the side of any term then the sign of the term also changes. Positive terms become negative and the negative terms become positive.