I don't understand how to solve a problem by "completing the square"

Question

Here is an example problem

1. m² + 10m + 7 = 0

I don't understand how to solve it like this...

Answer 1

m² + 10m + 7 = 0

Step 1: subtract 7 from both sides: m² + 10m = -7

Step 2: Divide 10 by 2 to get 5 and then add 5² = 25 to both sides: m² + 10m + 25 = 18

Step 3: Factor the left side as a perfect square: (m + 5)² = 18

Step 4: Take square roots of both sides and solve for m: m + 5 = ±√18

m = -5 ± √18 = -5 ± 3√2