What is the perimeter of quadrilateral ABCD?

23.1 or 18+√26 units.

Step-by-step explanation:

First, you would find the distance of AB which is you can just count because it is a straight line: 7 units.  Just skip BC for now, I'll come back to it later.  To find CD, you do the same thing and would get 6 units.  Then, for DA or AD you do it again and get 5.  Now for BC you would use the distance formula, if you do not know this yet, I will have a different method below this.

 The distance formula is : d=√((x₂-x₁)²+(y₂-y₁)²) Now X₂ would be the               x-coordinate of B which is 4.  X₁ would be the x-coordinate of C which is 3.  Y₂ would be the y-coordinate of B which is 2 while Y₁ is the y-coordinate of C which would be -3.  Finally you plug this into the equation which would be  d=√((4-3)²+(2-(-3))²) which equals √26 or 5.1 if you round it.  Finally, you would add all the side lengths which would be 7, 6, 5 and 5.1 or √26.  Which gets you 23.1 or 18+√26 units.

Now if you don't know the distance formula, you would use the pythagorean theorem.  First, you would draw an imaginary straight line down from point B to the same y-coordinate as C, getting you to the point (4,-3).  The distance from B to that point would be 5 units.  Then you draw another imaginary line from point C to (4,-3) . The distance from that would be 1.  Now, you can use the pythagorean theorem with BC being the hypotenuse and 5 and 1 being the legs.  5²+1²=c².     c²=26     c=√26

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11