Question

How do you solve the equation $2{x^2} - 512 = 0$?

Answer 1

Hint: The above equation is a quadratic equation, which includes the concept of square root and basic mathematical operations for solving the equation.
In literal meaning square root means, when an integer is raised to power half.
Using the basic mathematical calculations we will solve the given equation.

Complete step-by-step solution:
Let’s discuss a few mathematical basics in order to better understand the problem.
When a whole number is shifted from RHS to LHS and LHS to RHS its sign changes, that is from positive to negative and negative to positive. When an equation contains a variable then we must separate the variable on one side and constant on one side. If the coefficient of variable is one then the value of the variable can be calculated directly, if the coefficient of variable is more than one, then that constant value must be divided with the other constant value which was separated.
The same basics we will apply in order to solve the given equation.
$ \Rightarrow 2{x^2} - 512 = 0$
$ \Rightarrow 2{x^2} = 512$ (We have shifted the constant term on RHS)
$ \Rightarrow {x^2} = \dfrac{{512}}{2}$ (We have divided the coefficient of x with constant term which we had shifted on RHS)
$ \Rightarrow {x^2} = 256$ (We have removed the square root now)
$ \Rightarrow x = \sqrt {256} $
$ \Rightarrow x = \pm 16$

Therefore the value of $x$ is $\pm 16$ .

Note: In order to solve such problems we must remember a few square roots which are common to use, as of 121, 169, 196 , 225 , 256 , 289 (11, 13 , 14, 15, 16, 17 are their square roots). Like the square root means power half in the similar manner cube root means power 1/3.