x^2-5+7=0

To solve the equation \( x^2 - 5 + 7 = 0 \), we can first simplify it:

\[ x^2 + 2 = 0 \]

Next, we can rearrange the equation to isolate \( x^2 \):

\[ x^2 = -2 \]

Now, to solve for \( x \), we take the square root of both sides. Remember that square roots of negative numbers involve imaginary numbers:

\[ x = \pm \sqrt{-2} = \pm i \sqrt{2} \]

Thus, the solutions to the equation \( x^2 - 5 + 7 = 0 \) are:

\[ x = i \sqrt{2} \quad \text{and} \quad x = -i \sqrt{2} \]