Solve for x over the real numbers:
2 x^2 - 17 x - 1 = 0
Divide both sides by 2:
x^2 - (17 x)/2 - 1/2 = 0
Add 1/2 to both sides:
x^2 - (17 x)/2 = 1/2
Add 289/16 to both sides:
x^2 - (17 x)/2 + 289/16 = 297/16
Write the left hand side as a square:
(x - 17/4)^2 = 297/16
Take the square root of both sides:
x - 17/4 = (3 sqrt(33))/4 or x - 17/4 = -(3 sqrt(33))/4
Add 17/4 to both sides:
x = 17/4 + (3 sqrt(33))/4 or x - 17/4 = -(3 sqrt(33))/4
Add 17/4 to both sides:
Answer: x = 17/4 + (3 sqrt(33))/4 or x = 17/4 - (3 sqrt(33))/4