5T^2-10T+4=0

Question

Solve the quadratic equation by completing the squares:

Answer 1

5t^2 - 10t + 4 = 0

t^2 - 2t + 4/5 = 0

There's a -2 on the t in the middle.  Half of -2 is -1.  -1 squared is 1.

t^2 - 2t + 1 - 1 + 4/5 = 0

(t - 1)^2 - 1 + 4/5 = 0

(t - 1)^2 - 5/5 + 4/5 = 0

(t - 1)^2 - 1/5 = 0

(t - 1)^2 = 1/5

t - 1 = +- sqrt(1/5)

t = +- 1/sqrt(5) + 1

t = +- sqrt(5)/5 + 1

t = -sqrt(5)/5 + 1   or   t = sqrt(5)/5 + 1