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Solve each of the following equations: (10) x^2 + x / sqrt 2 + 1 = 0

Solve each of the following equations: 

Q: 10        x^2+\frac{x}{\sqrt{2}}+1=0

 

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Given equation is
x^2+\frac{x}{\sqrt{2}}+1=0 
Now, we know that the roots of the quadratic equation are given by the formula
\frac{-b\pm \sqrt{b^2-4ac}}{2a}
In this case the value of a = 1 , b =\frac{1}{\sqrt2} \ and \ c= 1
Therefore,
\frac{-\frac{1}{\sqrt2}\pm \sqrt{(\frac{1}{\sqrt2})^2-4.1.1}}{2.1}= \frac{-\frac{1}{\sqrt2}\pm\sqrt{\frac{1}{2}-4}}{2} = \frac{-\frac{1}{\sqrt2}\pm\sqrt{-\frac{7}{2}}}{2}=\frac{-1\pm\sqrt{7}i}{2\sqrt2}
Therefore, the solutions of the equation are 

 \frac{-1\pm\sqrt{7}i}{2\sqrt2}

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