Solve the following quadratic function by completing the square \[ y=x^{2}-8 x+5 \] \( x=[?] \pm \sqrt{\square]} \)

To complete the square for the quadratic function \( y = x^2 - 8x + 5 \), we first focus on the \( x^2 - 8x \) part. Take half of the coefficient of \( x \) (which is -8), square it, giving you \( (-4)^2 = 16 \). Now, rewrite the equation: \[ y = (x^2 - 8x + 16) - 16 + 5 \] \[ y = (x - 4)^2 - 11 \] Now, to find \( x \) in terms of \( y \): \[ (x - 4)^2 = y + 11 \] Taking the square root gives: \[ x - 4 = \pm \sqrt{y + 11} \] Finally, solving for \( x \): \[ x = 4 \pm \sqrt{y + 11} \] So your answer is: \( x = 4 \pm \sqrt{y + 11} \)