Question

X2 - 2x + 2 = 0

Answer 1

Answer:

Step-by-step explanation:

Let's solve x^2 - 2x + 2 = 0 using "completing the square:"

1.  Take the coefficient of x:  It is -2.

2.  Halve this, obtaining -1.

3.  Square this result, obtaining 1.

4.  Add 1, and then subtract 1, between -2x + 2:

    x^2 - 2x + 1 - 1 + 2 = 0

5.  Rewrite x^2 - 2x + 1 + 1 = 0 beginning with the square of a binomial

    (x - 1)^2 + 1 = 0, or (x - 1)^2 = -1

6.  Take the square root of both sides, obtaining x - 1 = ±i, or x = 1 ±i

7.  Write out the roots:  they are x = 1 + i and x = 1 - i (two complex, different roots).  No real roots, so the last command of this question is irrelevant.  The graph never touches the x-axis; the graph is in Quadrants I and II and is that of a parabola that opens up.