that formula is:
-b plus or minus square root of (b^2 - 4ac)
x = -----------------------------------------------
2a
the equation needs to be put in standard form of ax^2 + bx + c = 0
it's already in standard form.
this means that a = 1, b = -2, c = 2
plug those values into the quadratic formula and you get:
2 plus or minus square root of (4 - 4*1*2))
x = -----------------------------------------------
2*1
you get:
2 plus or minus square root of (-4)
x = -----------------------------------------------
2
square root of (-4) is equal to square root of (4 * (-1)) which is equal to 2 * square root of (-1).
square root of (-1) is equal to the letter i.
therefore square root of (-4) is equal to 2*i.
the value of the equation is equal to 0 when:
x = (2 + 2*i)/2 or x = (2 - 2*i)/2
simplify this to get:
x = 1 + i or x = 1 - i
use of a quadratic equation solver online confirms the solution is correct, as shown below:
