To solve this problem, you need to set the equations equal to each other and solve for t.

10t^2 = 4 + 2t^2
10t^2 - 2t^2 = 4
8t^2 = 4
t^2 = 4/8
t^2 = 1/2
t = ±√(1/2)
t = ±1/√2

Now, substitute this value of t into the third equation:

x = -5 - 8t + t^2/2
x = -5 - 8(±1/√2) + (1/(2√2))/2
x = -5 ± 4/√2 + 1/(4√2)
x = -5 ± 4/√2 + 1/√2
x = -5 ± (4 + 1)/√2
x = -5 ± 5/√2

Therefore, the solutions for x are x = -5 + 5/√2 and x = -5 - 5/√2.