How do we solve $ 2{x^2} - x - 10 = 0 $ ?

Hint: According to the question, first we will arrange the equations and then start removing the constant by adding or subtracting some other constant on both sides. And when in the Right Hand Side, only left 0 then we can calculate the square root by each of the factors of L.H.S separately.

Complete step by step solution:
The given equation is as:
 $ 2{x^2} - x - 10 = 0 $
Now, we will reorder the terms of equation
On factorising we get
 $ 2{x^2} + 4x - 5x - 10 = 0 $
0n taking factor on the left side we get
 $ (2x - 5)(x + 2) = 0 $
Now, calculate the square root by each of the factors separately.
Break this problem into two cases by setting $ (2x - 5) $ and $ (x + 2) $ equal to 0 and 0.
In case-1:
 $ 2x - 5 = 0 $
 $ \Rightarrow x = \dfrac{5}{2} $
In case-2:
 $ x + 2 = 0 $
 $ \Rightarrow x = - 2 $
Therefore, the solution to the question is based on the solutions from the cases.
 $ x = \{ \dfrac{5}{2}, - 2\} $
So, the correct answer is “ $ x = \{ \dfrac{5}{2}, - 2\} $ ”.

Note: There are other methods to compute square root by Long Division Method. Any number can be communicated as a result of prime numbers. This strategy for portrayal of a number as far as the result of prime numbers is named as prime factorization method. It is the most straightforward technique known for the manual computation of the square base of a number.