solve...x=2+rad8-x?

Question

8-x is on one 1

a parallel system of equations has ________ solutions

Answer 1

x=2+rad8-x

Assuming by "rad" you mean "radical" (square root), I'll write that sqrt(8) in computer-language fashion:

x = 2 + sqrt(8) - x
x + x = 2 + sqrt(8) - x + x
2x = 2 + sqrt(8)
2x = 2 + sqrt(4*2)
2x = 2 + sqrt(4)*sqrt(2)
2x = 2 + 2*sqrt(2)
2x/2 = (2 + 2*sqrt(2))/2
x = 1 + sqrt(2)

Note that I'm assuming you mean the radical applies only to the 8. If it also includes the -x, the solution is different:

x = 2 + sqrt(8 - x)
x - 2 = sqrt(8 - x)
(x - 2)^2 = sqrt(8-x)^2
x^2 - 4x + 4 = 8 - x
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0

x = 4 or x = -1

x=4 works in the obvious fashion:

x = 2 + sqrt(8 - x)
4 = 2 + sqrt(8-4)
4 = 2 + sqrt(4)
4 = 2 + 2

x=-1 works when you use the negative root:

x = 2 + sqrt(8 - x)
-1 = 2 + sqrt(8 - (-1))
-1 = 2 + sqrt(8 + 1)
-1 = 2 + sqrt(9)
-1 = 2 + -3

Answer 2

??

Answer 3

huh wat wat huh