e^(-x^2/2)=1/2

e^{(-1/2)x^2}= 1/2       take the natural log of both sides

ln e^{(-1/2)x^2}  = ln (1/2)    and by a property of logs - and remembering that ln e = 1 - we can write

(-1/2)x^2 =    ln(1/2)    multiply both sides by -2

x^2 = -2ln(1/2)

x^2 = about 1.38629        take the square root of both sides

x = about  ±1.1774