Complete the square:
(2 x^2)/5-8 x+1
Group terms containing x, leaving a blank spot to add a constant in later:
((2 x^2)/5-8 x+ )+1
((2 x^2)/5-8 x+ ) = 2/5 (x^2-20 x^2+ ):
(2 (x^2-20 x+ ))/5+1
Take one half of the coefficient of x and square it. Multiply by the outside factor 2/5, then add and subtract.
Add and subtract 2/5 ((-20)/2)^2 = 40:
2/5 (x^2-20 x+100)+1-40
1-40 = -39:
2/5 (x^2-20 x+100)+-39
x^2-20 x+100 = (x-10)^2:
Answer: | 2/5 (x-10)^2-39
