 Hello friends welcome to the session I am Malkan today we are going to find the roots of the following quadratic equation if they exist By the method of completing the square our given equation is 2x square plus x minus 4 equal to 0 Let's start with the solution our equation is 2x square plus x minus 4 equal to 0 In the first step we'll divide the whole equation by 2. This will give us x square plus x by 2 minus 4 by 2 equal to 0 Now this implies x square Plus x by 2 Equal to 2 we have shifted the constant term to RHS Now we'll add 1 by 4 square on both the sides LHS and RHS this can be written as x square plus 2 into 1 by 2 into x plus 1 by 4 whole square Equal to 1 by 4 whole square plus 2 now This can be written as x plus 1 by 4 whole square equal to 1 upon 16 plus 2 This we have done by writing the whole square of LHS Now we'll take the square root of both the sides This can also be written as x plus 1 by 4 Whole square equal to on taking 16 as LCM we get 33 by 16 Now we'll take the square root of both the sides This can this implies x plus 1 by 4 equal to Square root of 33 upon 16 that is equal to 33 Plus minus 33 by 4 this implies x equal to 33 by 4 minus 1 by 4 or we can say x equal to minus 33 by 4 minus 1 by 4 this implies x equal to third square root of 33 minus 1 by 4 or x equal to minus 33 minus 1 by 4 Hence the roots are Minus 1 plus square root of 33 by 4 and minus 1 minus square root of 33 by 4 This is the required solution of the given equation. Hope you understood it and enjoyed the session. Goodbye and take care