Question

solve using the quadratic form
$x^2 - 2x + 2 = 0$.

Explanation:

Step1: Identify a, b, c values

For $ax^2+bx+c=0$, here $a=1$, $b=-2$, $c=2$

Step2: Recall quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Compute discriminant

$\Delta = b^2-4ac = (-2)^2-4(1)(2)=4-8=-4$

Step4: Substitute into formula

$$x=\frac{-(-2)\pm\sqrt{-4}}{2(1)}=\frac{2\pm2i}{2}$$

Step5: Simplify the expression

$x=\frac{2(1\pm i)}{2}=1\pm i$

Answer:

$x=1+i$ and $x=1-i$