Answer:
x = 7/10 + sqrt(409)/10 or x = 7/10 - sqrt(409)/10
Step-by-step explanation by completing the square:
Solve for x:
5 x - 7 - 18/x = 0
Bring 5 x - 7 - 18/x together using the common denominator x:
(5 x^2 - 7 x - 18)/x = 0
Multiply both sides by x:
5 x^2 - 7 x - 18 = 0
Divide both sides by 5:
x^2 - (7 x)/5 - 18/5 = 0
Add 18/5 to both sides:
x^2 - (7 x)/5 = 18/5
Add 49/100 to both sides:
x^2 - (7 x)/5 + 49/100 = 409/100
Write the left hand side as a square:
(x - 7/10)^2 = 409/100
Take the square root of both sides:
x - 7/10 = sqrt(409)/10 or x - 7/10 = -sqrt(409)/10
Add 7/10 to both sides:
x = 7/10 + sqrt(409)/10 or x - 7/10 = -sqrt(409)/10
Add 7/10 to both sides:
Answer: x = 7/10 + sqrt(409)/10 or x = 7/10 - sqrt(409)/10
