x^2 + 4 = 0
Using the square root method, subtract 4 from both sides.
x^2 = -4
To clear the power of 2, take the square root of both sides.
x = + - square rot of (-4)
x = + - 2i
This is a complex answer because the radicand was a negative number.
x^2 - 6x + 1 = 0
I would use completing the square to solve this problem.
Subtract 1 from both sides.
x^2 - 6x = -1
When completing the square, take the b term (-6) and divide by 2 (-6/2= -3),
then square this number (9), add the number to both sides.
x^2 - 6x + 9 = -1 + 9
The left side is now a perfect square trinomial.
(x - 3)^2 = 8
To clear the power of 2, take the square root of both sides.
x - 3 = + - sqrt 8
add 3 to both sides and simplify sqrt 8
x = 3 + - 2sqrt2
