Here, you will solve more complicated equations involving perfect squares.
There are two basic approaches you can use to solve an equation like [beautiful math coming... please be patient] $\,(3x+2)^2 = 16\,$:
To use this approach, you must:
[beautiful math coming... please be patient] $\,(3x+2)^2 = 16\,$  (original equation) 
[beautiful math coming... please be patient] $\,(3x+2)^2 16 = 0\,$  (need $\,0\,$ on one side; subtract $\,16\,$ from both sides) 
[beautiful math coming... please be patient] $(3x+2)^2  4^2 = 0$  (rewrite, so it's clear you have a difference of squares) 
[beautiful math coming... please be patient] $(3x+2+4)(3x+24) = 0$  (factor the difference of squares) 
[beautiful math coming... please be patient] $(3x+6)(3x2) = 0$  (simplify) 
[beautiful math coming... please be patient] $3x+6 = 0\ \ \text{or}\ \ 3x2 = 0$  (use the zero factor law) 
[beautiful math coming... please be patient] $3x = 6\ \ \text{or}\ \ 3x = 2$  (solve the simpler equations) 
[beautiful math coming... please be patient] $\displaystyle x = 2\ \ \text{or}\ \ x = \frac{2}{3}$  (solve the simpler equations) 
$(3(2)+2)^2\ \ \overset{\text{?}}{=}\ \ 16$  $(3(\frac{2}{3})+2)^2\ \ \overset{\text{?}}{=}\ \ 16$ 
$(6 + 2)^2 \ \ \overset{\text{?}}{=} \ \ 16$  $(2 + 2)^2 \ \ \overset{\text{?}}{=} \ \ 16$ 
$(4)^2 \ \ \overset{\text{?}}{=} \ \ 16$  $(4)^2 \ \ \overset{\text{?}}{=} \ \ 16$ 
$16 = 16$ Check!  $16 = 16$ Check! 
The basic idea is that you're (correctly!) ‘undoing’ a square with the square root.
Notice that if
[beautiful math coming... please be patient]
$\,k\lt 0\,$,
then the equation $\,z^2 = k\,$ has no real number solutions.
For example, consider the equation
[beautiful math coming... please be patient]
$\,z^2 = 4\,$.
There is no real number which, when squared, gives $\,4\,$.
To use this approach, you must:
[beautiful math coming... please be patient] $(3x+2)^2 = 16$  (original equation) 
[beautiful math coming... please be patient] $3x + 2 = \pm\sqrt{16}$  (check that $\,k\ge 0\,$; use the theorem) 
[beautiful math coming... please be patient] $3x + 2 = \pm 4$  (simplify: $\,\sqrt{16} = 4\,$) 
[beautiful math coming... please be patient] $3x + 2 = 4\ \ \text{or}\ \ 3x + 2 = 4$  (expand the ‘plus or minus’ shorthand) 
[beautiful math coming... please be patient] $3x = 2\ \ \text{or}\ \ 3x = 6$  (subtract $\,2\,$ from both sides of both equations) 
[beautiful math coming... please be patient] $\displaystyle x = \frac{2}{3}\ \ \text{or}\ \ x = 2$  (divide both sides of both equations by $\,3\,$) 
For more advanced students, a graph is displayed.
For example, the equation $\,(3x+2)^2 = 16\,$
is optionally accompanied by the
graph of $\,y = (3x+2)^2\,$ (the left side of the equation, dashed green)
and the graph of
$\,y = 16\,$ (the right side of the equation, solid purple).
In this example, you are finding the values of $\,x\,$ where the green
graph intersects the purple graph.
Click the “show/hide graph” button if you prefer not to see the graph.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
