$x^{2} = - 7 - \sqrt{10} x$

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Solution

Given: $x^{2} = - 7 - \sqrt{10} x$

On transposing all the terms of the right-hand side to the left-hand side, we get:

$x^{2} + 7 + \sqrt{10} x = 0 \Rightarrow x^{2} + \sqrt{10} x + 7 = 0$

Thus, the standard form of the given quadratic equation is $x^{2} + \sqrt{10} x + 7 = 0$ .

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