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)
+37146 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
