Solve $x^2+6x+2$

Step-by-step solution

1. Step 1 · Completing the square
   $$x^2+6x=(x+3{)}^2-9$$

   Half of 6 is 3; adding and subtracting 9 keeps the value unchanged.

2. Step 2 · Reinstate the constant
   $$(x+3{)}^2-9+2$$

   Bring the original +2 back into the expression.

3. Step 3 · Simplify
   $$(x+3{)}^2-7$$

   Vertex form shows a minimum of −7 at x = −3.