Solve by the square root property. (-x^2+1)^2 = 4

Question

how do i solve this? 

Answer 1

By the square root property, the first step is to square root both sides, giving us: 

 

-x^2 + 1 = 2   OR   -x^2 + 1 = - 2

 

Solving for x in the first equations gives us -x^2 = 1, so x^2 = - 1. This is impossible unless we are solving over complex numbers. If we are, then x = i, - i. 

 

Now let's turn to the second equation. -x^2 = - 3, so x^2 = 3, and x = √3 or - √3.