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