Solve the equation by completing the square.

Question

x^2-2=9x
My answer: x=9/2+or- the sqrt. of 22.25
(but when I checked my answer the actual answer was x=9+or - the sqrt. of 89 and then all over 2)
Please explain why my answer is different from the actual answer.

Answer 1

x^2 - 9x = 2
x^2 - 9x + (9/2)^2 = 2 + (9/2)^2
(x - 9/2)^2 = 89/4
x = 9/2 ± √(89/4)
x = 9/2 ± √22.25

but you could also factor out the 1/4 in 89/4 and say

x = 9/2 ± √89/√4
x = 9/2 ± √89/2
x = (9 ± √89)/2

these exercises usually want things as fractions rather than decimals, and the quadratic formula usually expresses the answers as they did.