For what value of x would the expression

5x - 18/x - 7

A.-7

B. 0

C. 1/7

D. 7

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