 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question here says solve each of the following equations. Ninth equation is x squared plus x plus 1 divided by root 2 equal to 0. In this question we have to solve the equation x squared plus x plus 1 by root 2 equal to 0. Now before starting with the solution we see the key idea behind the question. We see that solution to a quadratic equation ax squared plus bx plus c equal to 0 where a is not equal to 0 is given by x equal to minus b plus minus under the root b squared minus 4ac the whole divided by 2a. This is same as minus b plus minus under the root 4ac minus b squared i eta the whole divided by 2a. Now let us start with the solution to this question. The equation given to us is x squared plus x plus 1 by root 2 equal to 0. Now if we compare this equation with x because bx plus c equal to 0 we get a is equal to 1, v is equal to 1 and c equal to 1 by root 2. So we can easily find out the value of b squared minus 4ac that becomes 1 square minus 4 into 1 into 1 by root 2 which is same as 1 minus 4 by root 2. Now on simplifying it we get 1 minus 4 root 2 divided by 2 that is equal to 1 minus 2 root 2. Therefore x can be written as minus 1 plus minus under the root 1 minus 2 root 2 divided by 2 into 1. This is same as minus 1 plus minus under the root 2 root 2 minus 1 i eta divided by 2. Therefore our answer to this question is minus 1 plus minus under the root 2 root 2 minus 1 i eta by 2. I hope you understood the question. I enjoy the session. Goodbye.