Need help solving an algebra review problem for AP physics!!

Question

v²_{f= v}²₀+ 2aΔx

Solve for v₀ if V_f = 0

Answer 1

v_f² = v₀² + 2aΔx

v₀² = v_f² - 2aΔx

v₀ = √(v_f² - 2aΔx)

v_f = 0 ⇒

v₀ = √(-2aΔx)

Note that the acceleration 'a' must be negative, since the object slows down from v₀>0 to v_f=0. Furthermore, Δx is a distance (i.e. positive), so the argument of the square root is positive.