I need help finding the length of a pendulum string.

A pendulum consists of a string of length L with a mass m on the end. When the pendulum is released from rest, it has a period of oscillation T. The string is then lengthened by 0.565 m, and the period is 0.468 seconds longer.

T = 2π√L/g = [2π/√g]√L = 2.0061√L <= T
T² = 4.02444L <= T²
---
T+0.468 = 2.0061√(L+0.565)
(T+0.468)² = T² + 0.936T + 0.219024
[2.0061√(L+0.565)]² = 4.02444(L + 0.565) = 4,02444L +2.27381
T² + 0.936T + 0.219024 = 4.0244L + 2.27381 <= Eq # 2
---
4.0244L + 0.936(2.0061√L) = 4.0244L + 2.054786
1.87771√L = 2.054786
√L = 2.054786/1.87771 = 1.09430
L = 1.1975 m <= ANS
===== check ANS ====
T = 2π√L/g = 2π√1.1975/9.81 = 2.1952 s {L = 1.20 m}
T = 2π√1.7625/9.81 = 2.6632 s {L = 1.1975 + 0.565}
ΔT = 2.6632 - 2.1952 = 0.4680 s ANS is correct