Answer:
f(x) = (x - 1/5)² + 9/25
Explanation:
f(x) = -5x² + 2x - 2
to make a complete square,
move the constant to the other side,
-5x² + 2x = 2
divide the whole expression by -5,
x² - 2/5 x = -2/5
divide the x term by 2 to get it's half, 2/5 / 2 = 2/5 * 1/2 = 1/5
square the half of the x term and add it to both sides of the equation, (1/5)² = 1/25
x² - 2/5x + 1/25 = -2/5 + 1/25
x² - 2/5x + 1/25 = -9/25
now we have a perfect square, as (a - b)² = a² + b² - 2ab
thus,
f(x) = (x - 1/5)² + 9/25