Question

How do you solve \[{n^2} = 6n\] ?

Answer 1

Hint: The given equation is a quadratic equation in one variable $ n $ . Solving this equation means finding the value of $ n $ which satisfies the equation, i.e. such values for which LHS of the equation is equal to the RHS of the equation. In a second degree equation we get two values of the variable as a solution.

Complete step-by-step answer:
We have to solve the equation \[{n^2} = 6n\].
The given equation is a quadratic equation in one variable $ n $ . We have to find the values of $ n $ which satisfies the equation.
To solve the equation we first transfer all the terms to one side, to LHS in this case, as follows,
 $
  {n^2} = 6n \\
   \Rightarrow {n^2} - 6n = 0 \;
 $
We can take $ n $ common from both the terms and write it as,
 $
  {n^2} - 6n = 0 \\
   \Rightarrow n(n - 6) = 0 \;
 $
We get $ n(n - 6) = 0 $ , which means
 $
  n = 0\;\;or\;\;(n - 6) = 0 \\
   \Rightarrow n = 0\;\;or\;\;\;n = 6 \;
 $
We get $ n = 0 $ or $ n = 6 $ . This means that $ n $ can take either of both the values to satisfy the equation.
While solving a quadratic equation we get two values in the solution.
Hence, the solution of the given equation \[{n^2} = 6n\] is $ n = 0 $ or $ n = 6 $ .
So, the correct answer is “$ n = 0 $ or $ n = 6 $ ”.

Note: When the highest power of the variable in an equation is $ 2 $ it is a quadratic equation. While transferring terms to the other side the arithmetic signs are reversed, i.e. ‘ $ + $ ’ becomes ‘ $ - $ ’ and vice-versa. We get two values of the variable in the solution.
Also, we can check the solution by putting the values in the equation.
For $ n = 0 $ , $ LHS = {n^2} = {0^2} = 0 $ and $ RHS = 6n = 6 \times 0 = 0 $ . Thus, LHS = RHS.
For $ n = 6 $ , $ LHS = {n^2} = {6^2} = 36 $ and $ RHS = 6n = 6 \times 6 = 36 $ . Thus, LHS = RHS.
Hence, our solution is correct.