Simplify $(x + 1)^{2} = 2 (x - 3)$ and check whether it is a quadratic equation.

Open in App

Solution

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

The given equation is $(x + 1)^{2} = 2 (x - 3)$ can be simplified as follows:

$(x + 1)^{2} = 2 (x - 3) \Rightarrow x^{2} + 1 + 2 x = 2 x - 6 (∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b) \Rightarrow x^{2} + 1 + 2 x - 2 x + 6 = 0 \Rightarrow x^{2} + 7 = 0$

Since the equation $x^{2} + 7 = 0$ is of the form $a x^{2} + b x + c = 0$ .

Hence, the equation $(x + 1)^{2} = 2 (x - 3)$ is a quadratic equation.

Suggest Corrections

Similar questions

(2 x - 1) (x - 3) = (x + 5) (x - 1)

x (x + 6) = 0

(x + 1)^{2} = 2 (x - 3)

{(x + 1)}^{2} = 2 (x - 3)

(x + 1)^{2} = 2 (x - 3)

Join BYJU'S Learning Program