Question

What are the solutions of x2 -2x+2=0​

Answer 1

Answer: x = 1 ± i

Step-by-step 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 = $\frac{2 + \sqrt{4-8} }{2}$ or  $\frac{2 - \sqrt{4-8} }{2}$

x = $\frac{2 + \sqrt{-4} }{2}$ or $\frac{2 - \sqrt{-4} }{2}$

Recall ; $\sqrt{-4}$ can be written as $\sqrt{-1}$ X $\sqrt{4}$, and $\sqrt{-1}$ = i

Substituting this

x = $\frac{2+2i}{2}$ or $\frac{2-2i}{2}$

simplifying, we have

x = 1 + i or 1 - i