Which of the following is a solution of x2 − 6x = –22?

a) negative 6 minus i square root of 52
b) negative 6 plus i square root of 13
c) 3 minus i square root of 13
d) negative 3 plus i square root of 52

C) 3 - i√13

Step-by-step explanation:

x² - 6x = -22

x² - 6x + (-6/2)² = -22 + (-6/2)²

x² - 6x + 9 = -22 + 9

(x - 3)(x - 3) = -13

x - 3 = ± √-13

x - 3 = ± i√13

x = 3 ± i√13

x = 3 + i√13 & x = 3 - i√13

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough