Answer:
x = 5/2 + sqrt(17)/2 or x = 5/2 - sqrt(17)/2
Explanation:
Solve for x:
x^2 - 5 x + 2 = 0
Subtract 2 from both sides:
x^2 - 5 x = -2
Add 25/4 to both sides:
x^2 - 5 x + 25/4 = 17/4
Write the left hand side as a square:
(x - 5/2)^2 = 17/4
Take the square root of both sides:
x - 5/2 = sqrt(17)/2 or x - 5/2 = -sqrt(17)/2
Add 5/2 to both sides:
x = 5/2 + sqrt(17)/2 or x - 5/2 = -sqrt(17)/2
Add 5/2 to both sides:
Answer: x = 5/2 + sqrt(17)/2 or x = 5/2 - sqrt(17)/2