Please help me to transform this to vertex form: y=5x^2-2x+2?

y = 5x² - 2x + 2
y = 5[x² - (2/5)x] + 2
y = 5[x² - 2(1/5)x + (1/5)²] - 5(1/5)² + 2

The vertex form :
y = 5[x - (1/5)]² + (9/5)

y = 5x² - 2x + 2

factor out the leading coefficient
y = 5(x² - ⅖x) + 2

complete the square
 coefficient of the x term: -⅖
 divide it in half: -⅕
 square it: (-⅕)² = (⅕)²
 use (⅕)² to complete the square:
y = 5(x² - ⅖x + (⅕)²) - 5(⅕)² + 2
 = 5(x - ⅕)² - ⅕ + 2
 = 5(x - ⅕)² + 1⅘

vertex: (⅕, 1⅘)

y = 5 [ x² - (2/5) x ] + 2
y = 5 [ x² - (2/5) x + 1/25 ] - 1/5 + 2
y = 5 [ x - 1/5 ] ² + 9/5