xto the second/2=x+1?

Answer 1

move all values to one side of the equation and solve from there:

x²/2 - x - 1 = 0

x² - 2x - 2 = 0 { Mulitply both sides by 2 }

(2 +/- √(4 + 8)) / 2 { Quadratic formula }

(2 +/- 2√3) / 2 { Simplify }

1 +/- √3

Answer 2

X^2/2 = x +1
multiply both sides by 2
x^2 = 2x + 2
or x^2 - 2x -2 = 0

using the quadratic formula:
x = -b +/- (sq.root of b^2 - 4 ac) / 2

x = 1 +/- sq. root 3

Answer 3

(x^2)/x = x + 1
x^2 = x(x + 1)
x^2 = x^2 + x
0 = x

not possible because x is also a denominator of one side which is not possible because it leaves the number undefined

Answer 4

1/2 x^2=x+1
x^2=2x+2
x^2-2x-2=0
x=(2+/-√(4+8))/2
x=1+/-1/2 √12
x=1+/-√3
x=1+√3, 1-√3

Answer 5

x^2=2(x+1)
x^2=2x+2

-b+(-)_/(b^2-4ac)
---------------------
2a

x^2-2x-2=0

-(-2)+(-)_/((-2)^2-(4)(1)(-2)
---------------------------------
2(1)

2+(-)_/(4)-(-8)
----------------
2

(2+-_/12)/2

[2+-2_/(3)]/2

(1+-_/3)