Check whether $x (x + 1) + 8 = (x + 2) (x - 2)$ is a quadratic equation.

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Solution

Given that: $x (x + 1) + 8 = (x + 2) (x - 2)$
By simplifying we get
$x^{2} + x + 8 = x^{2} - 4 x^{2} - x^{2} + x + 8 + 4 = 0 x + 12 = 0$
It is not of the form $a x^{2} + b x + c = 0$
The variable x is only in the first degree.
$∴$ It is not a quadratic equation.

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