In the following, determine the value of $k$ for which the given value is a solution of the equation
$x^{2} + 2 a x - k = 0, x = - a$

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Solution

Since, $x = - a$ is a root of the equation $x^{2} + 2 a x - k = 0$

Now put the value of $x = - a$ in the given equation.
we get,

$a^{2} + 2 a \times - a - k = 0 \Rightarrow k = - a^{2}$

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