Simplify $(x + 2) (x - 7) = 5$ and check whether it is a quadratic equation.

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Solution

We know that the general form of quadratic equation is $a x^{2} + b x + c = 0$ .

The given equation is $(x + 2) (x - 7) = 5$ can be simplified as follows:

$(x + 2) (x - 7) = 5 \Rightarrow x (x - 7) + 2 (x - 7) = 5 \Rightarrow x^{2} - 7 x + 2 x - 14 = 5 \Rightarrow x^{2} - 5 x - 14 - 5 = 0 \Rightarrow x^{2} - 5 x - 19 = 0$

Since the equation $x^{2} - 5 x - 19 = 0$ is of the form $a x^{2} + b x + c = 0$ .

Hence, the equation $(x + 2) (x - 7) = 5$ is a quadratic equation.

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