Yes, your work is correct.
The diagram does illustrate x²+6x+9=72. This is also represented by
(x+3)² = 72
We can take the square root of both sides:
[tex]\sqrt{(x+3)^2}=\sqrt{72}
\\
\\x+3=\pm 6 \sqrt2
\\
\\x+3-3=\pm 6 \sqrt{2} -3
\\
\\x=-3\pm 6\sqrt{2}[/tex]
When we evaluate this, the answers are x = -11.5 or x = 5.5.
