$(m+8)^{2}=72$

Step 1 ：Expand the left side of the equation: \((m+8)^{2} = m^{2} + 16m + 64\)

Step 2 ：Subtract 72 from both sides of the equation: \(m^{2} + 16m + 64 - 72 = 0\)

Step 3 ：Simplify the equation: \(m^{2} + 16m - 8 = 0\)

Step 4 ：Use the quadratic formula to solve for m: \(m = \frac{-16 \pm \sqrt{16^{2} - 4(1)(-8)}}{2(1)}\)

Step 5 ：Simplify under the square root: \(m = \frac{-16 \pm \sqrt{256 + 32}}{2}\)

Step 6 ：Simplify the square root: \(m = \frac{-16 \pm \sqrt{288}}{2}\)

Step 7 ：Factor out a 2 from under the square root: \(m = \frac{-16 \pm 2\sqrt{72}}{2}\)

Step 8 ：Simplify the equation: \(m = -8 \pm \sqrt{72}\)

Step 9 ：Write the final answer: \(\boxed{-8 + 6\sqrt{2}, -6\sqrt{2} - 8}\)