Question

How would you solve 25x^2-60x=-31 by "completing the square"?

The answer should be (6(+/-)sqrt5)/5. Not sure how to get it though.

Answer

25x^2 - 60x = -31

x^2 - 60x/25 = -31/25

x^2 - 12x/5 = -31/25

x^2 - 12x/5 + [(-12/5) / 2]^2 = -31/25 + [(-12/5) / 2]^2

x^2 - 12x/5 + 144/100 = -31/25 + 144/100

x^2 - 12x/5 + 36/25 = -31/25 + 36/25

(x - 6/5)(x - 6/5) = 5/25

(x - 6/5)^2 = 5/25

x - 6/5 = ± √(5 / 25)

x - 6/5 = ± √5 / 5

x = 6/5 ± √5/5

x = (6 ± √5) / 5

you're teacher is mean

this type of quadratic is solved easier with the quadratic formula

25x^2 - 60x + 31 = 0

a = 25

b = -60

c = 31

[-b ± √(b^2 - 4ac)] / 2a

(60 ± √500) / 50

(60 ± 10√5) / 50

x = (6 ± √5) / 5

Unanswered