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

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1 Answer

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.