Which are the solutions of x2 = 19x + 1?

StartFraction 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 19 EndRoot Over 2 EndFraction
StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction
StartFraction negative 19 minus StartRoot 19 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 19 EndRoot Over 2 EndFraction
StartFraction negative 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction negative 19 + StartRoot 365 EndRoot Over 2 EndFraction

Step-by-step explanation:

we have

we know that

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

StartFraction 19 minus StartRoot 365 EndRoot Over 2 EndFraction comma StartFraction 19 + StartRoot 365 EndRoot Over 2 EndFraction

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.