1. **State the problem:** Express the quadratic polynomial $2x^2 + 8x + 6$ in complete square form. 2. **Recall the formula:** A quadratic $ax^2 + bx + c$ can be written as $a(x - h)^2 + k$ where $(h, k)$ is the vertex. 3. **Factor out the coefficient of $x^2$ from the first two terms:** $$2x^2 + 8x + 6 = 2(x^2 + 4x) + 6$$ 4. **Complete the square inside the parentheses:** Take half of the coefficient of $x$, which is 4, half is 2, square it to get $2^2 = 4$. Add and subtract 4 inside the parentheses: $$2(x^2 + 4x + 4 - 4) + 6 = 2((x + 2)^2 - 4) + 6$$ 5. **Simplify:** $$2(x + 2)^2 - 8 + 6 = 2(x + 2)^2 - 2$$ 6. **Final answer:** The quadratic in complete square form is $$2(x + 2)^2 - 2$$ This matches the vertex at $(-2, -2)$ as given.