 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. Seventh equation is root 2 x square plus x plus root 2 equals to 0. In this question we have to solve the equation root 2 x square plus x plus root 2 equal to 0. Now before starting with the solution we see the key idea behind the question. Now solving a quadratic equation ax square plus bx 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 square minus 4ac the whole divided by 2a. This is the equation equal to minus b plus minus under the root 4ac minus b square the whole divided by 2a into ieta. Now we start with the solution to this question. The equation given to us is root 2 x square plus x plus root 2 equal to 0. Now if we compare this equation with ax square plus bx plus c equal to 0 we get a is equal to root 2 b is equal to 1 and c equal to root 2. So we can say that b square minus 4ac now becomes 1 square minus 4 into root 2 into root 2 and this is same as minus 7. From the key idea we see that x becomes equal to minus 1 plus minus under the root minus 7 divided by 2 root 2. So x equals to minus 1 plus minus under the root 7 ieta divided by 2 root 2. Therefore our answer to this question is minus 1 plus minus under the root 7 ieta divided by 2 root 2. I hope you understood the question and enjoyed the session. Goodbye.