Solve the equation by completing the square. Round to the nearest tenth, if necessary. Simplify your solutions and enter them from least to greatest, separated by a comma, if necessary. If there are no real solutions, enter no solutions. x2+6x−16=0

To solve the equation $x^2 + 6x - 16 = 0$ by completing the square, follow these steps:

1. Move the constant term to the other side of the equation: $x^2 + 6x = 16$

2. Find the value that completes the square: Take half of the coefficient of $x$, which is 6, divide it by 2 to get 3, and then square it to get 9. $\left(\frac{6}{2}\right)^2 = 3^2 = 9$

3. Add this value to both sides of the equation: $x^2 + 6x + 9 = 16 + 9$ $x^2 + 6x + 9 = 25$

4. Rewrite the left side as a perfect square: $(x + 3)^2 = 25$

5. Take the square root of both sides: $x + 3 = \pm 5$

6. Solve for $x$: $x + 3 = 5 \quad \text{or} \quad x + 3 = -5$ $x = 5 - 3 \quad \text{or} \quad x = -5 - 3$ $x = 2 \quad \text{or} \quad x = -8$

So, the solutions are $x = -8$ and $x = 2$.

Therefore, the solutions, from least to greatest, are: $-8, 2$