Math: Gauß Integral 2 (10 min)

Use $\int_{-\infty}^{\infty}dx e^{-x^2}=\sqrt{\pi}$ to prove the formula for the Gauß integral

$$\int_{-\infty}^{\infty}dx e^{-ax^2+bx}=\sqrt{\frac{\pi}{a}}e^{{b^2}/{4a}},\quad a>0.$$ (1)