Question

What are the solutions of x2 -2x+2=0​

Answer 1

Answer: x = 1 ± i

Explanation:

Solving the quadratic equation using the quadratic formula:

x =
`\frac{-b+\sqrt{b^(2)-4ac } }{2a}` or
`\frac{-b-\sqrt{b^(2)-4ac } }{2a}`

From the question :

a = 1

b = -2

c = 2

substituting inside the formula

X =
`\frac{-(-2)+\sqrt{(-2)^(2)-4(1)(2) } }{2(1)}` or

`\frac{-(-2) - \sqrt{2^(2)-4(1)(2) } }{2(1)}`

x =
`(2 + √(4-8) )/(2)` or
`(2 - √(4-8) )/(2)`

x =
`(2 + √(-4) )/(2)` or
`(2 - √(-4) )/(2)`

Recall ;
`√(-4)` can be written as
`√(-1)` X
`√(4)`, and
`√(-1)` = i

Substituting this

x =
`(2+2i)/(2)` or
`(2-2i)/(2)`

simplifying, we have

x = 1 + i or 1 - i