Answer:
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex]  or  [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
Step-by-step explanation:
So first you need to find the area of the swimming pool:
19*6 = 114
Next you add the area of the swimming pool and the area of the walkway:
114 + 770 = 884
After this you solve for x using this equation:
(19 +2x) * (6 + 2x) = 884
This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.
The step-by-step is this:
[tex]4x^{2} +50x+114=884[/tex]
[tex]4x^2+50x+114-884=884-884[/tex]
 [tex]4x^2+50x+114-884=0[/tex]
Now we'll use the quadratic formula to simplify it farther:
[tex]x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}[/tex]
[tex]x=\frac{-50 + or - \sqrt{14820} }{8}[/tex]
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
