#1**+1 **

Solve for x:

8 + 1/x = x

Bring 8 + 1/x together using the common denominator x:

(8 x + 1)/x = x

Multiply both sides by x:

8 x + 1 = x^2

Subtract x^2 from both sides:

-x^2 + 8 x + 1 = 0

Multiply both sides by -1:

x^2 - 8 x - 1 = 0

Add 1 to both sides:

x^2 - 8 x = 1

Add 16 to both sides:

x^2 - 8 x + 16 = 17

Write the left hand side as a square:

(x - 4)^2 = 17

Take the square root of both sides:

x - 4 = sqrt(17) or x - 4 = -sqrt(17)

Add 4 to both sides:

x = 4 + sqrt(17) or x - 4 = -sqrt(17)

Add 4 to both sides:

** x = 4 + sqrt(17) or x = 4 - sqrt(17)**

Guest Jun 1, 2019

#2**0 **

x = 1/x + 8 is what is being asked multiply by x

x^2 = 1+8x re-arrange

x^2-8x-1=0 use quadratic formula a = 1 b = -8 c = -1

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

{8+-sqrt(64+4(1)(1)) } / 2

4 +- sqrt(17*4)/2

4+- 2(sqrt17)/2

4 +- sqrt 17

ElectricPavlov Jun 2, 2019