 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question here says solve each of the following equations. 10th equation is x squared plus x by root 2 plus 1 is equal to 0. Now in this question we have to solve the equation x squared plus x by root 2 plus 1 equal to 0. Now before starting with the solution we see the key idea behind the question. Solution 2 a quadratic equation a x squared plus b x plus c equal to 0 where a is not equal to 0 is given by equal to minus b plus minus under the root b squared minus 4ac the whole divided by 2a. This is equal to minus b plus minus under the root 4ac minus b squared divided by 2a into a. Now let us start with the solution to this question. The equation given to us is x squared plus x by root 2 plus 1 equal to 0. Now if we compare this equation with a x squared plus b x plus c equal to 0 we get a equal to 1, b equal to 1 by root 2 and c equal to 1. Now we can easily find out the value of b squared minus 4ac that is equal to 1 by root 2 the whole square minus 4 into 1 into 1. This is equal to 1 by 2 minus 4 and this is equal to minus 7 by 2. Therefore x becomes minus 1 by root 2 plus minus of root of minus 7 by 2 the whole divided by 2. This is equal to minus 1 plus minus root 7 ieta divided by 2 root 2. Therefore our answer to this question is minus 1 plus minus root 7 ieta divided by 2 root 2. I hope you understood the question and enjoyed the session. Goodbye.