Solve the following quadratic equation by applying the quadratic formula `p^2x^2+(p^2-q^2)x-q^2=0`

Explanation

`x = (-(p^2 - q^2) +- sqrt((p^2- q^2)^2 + 4p^2q^2))/(2p^2) `

`= (q^2 - p^2 +- sqrt(p^4 + q^4-2p^2q^2 + 4p^2q^2))/(2p^2)`

`= (q^2 - p^2 +- sqrt(p^4 + q^2 + 2p^2q^2))/(2p^2)`

`= (q^2 - p^2 +- (p^2 + q^2))/(2p^2)`

`x = (q^2 - p^2 + p^2 + q^2)/(2p^2)`

and `x= (q^2 - p^2 - p^2 - q^2)/(2p^2)`

so, `x= q^2 /p^2 and x= -1`

Answer