Here, you will solve simple equations involving perfect squares.
There are two basic approaches you can use to solve an equation like
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$\,x^2  9 = 0\,$:
To use this approach, you must:
[beautiful math coming... please be patient] $x^2  9 = 0$  (original equation; check that $\,0\,$ is on one side of the equation) 
[beautiful math coming... please be patient] $(x+3)(x3) = 0$  (factor to get a product on the other side) 
[beautiful math coming... please be patient] $x+3 = 0\ \ \text{or}\ \ x3 = 0$  (use the zero factor law) 
[beautiful math coming... please be patient] $x=3\ \ \text{or}\ \ x = 3$  (solve the simpler equations) 
Notice that if
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$\,k\lt 0\,$,
then the equation $\,z^2 = k\,$ has no real number solutions.
For example, consider the equation
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$\,z^2 = 4\,$.
There is no real number which, when squared, gives $\,4\,$.
To use this approach, you must:
[beautiful math coming... please be patient] $x^2  9 = 0$  (original equation) 
[beautiful math coming... please be patient] $x^2 = 9$  (isolate a perfect square by adding $\,9\,$ to both sides) 
[beautiful math coming... please be patient] $x = \pm\sqrt{9}$  (check that $\,k\ge 0\,$; use the theorem) 
[beautiful math coming... please be patient] $x = \pm 3$  (rename: $\,\sqrt{9} = 3\,$) 
[beautiful math coming... please be patient] $x = 3\ \ \text{or}\ \ x = 3$  (expand the ‘plus or minus’ shorthand, if desired) 
Here are three slightly different approaches to solving the equation [beautiful math coming... please be patient] $\,16x^2  25 = 0\,$:
[beautiful math coming... please be patient] $16x^2  25 = 0$  (original equation) 
[beautiful math coming... please be patient] $(4x)^2  5^2 = 0$  (rewrite lefthand side as a difference of squares) 
[beautiful math coming... please be patient] $(4x + 5)(4x  5) = 0$  (factor the lefthand side) 
[beautiful math coming... please be patient] $4x + 5 = 0\ \ \text{or}\ \ 4x5 = 0$  (use the Zero Factor Law) 
[beautiful math coming... please be patient] $4x = 5\ \ \text{or}\ \ 4x = 5$  (solve the simpler equations) 
[beautiful math coming... please be patient] $\displaystyle x = \frac{5}{4}\ \ \text{or}\ \ x = \frac{5}{4}$  (solve the simpler equations) 
[beautiful math coming... please be patient] $16x^2  25 = 0$  (original equation) 
[beautiful math coming... please be patient] $16x^2 = 25$  (add $\,25\,$ to both sides) 
[beautiful math coming... please be patient] $\displaystyle x^2 = \frac{25}{16}$  (divide both sides by $\,16\,$: now, $x^2$ is isolated) 
[beautiful math coming... please be patient] $\displaystyle x = \pm\sqrt{\frac{25}{16}}$  (use the theorem) 
[beautiful math coming... please be patient] $\displaystyle x = \pm\frac{5}{4}$  (rename: [beautiful math coming... please be patient] $\,\sqrt{\frac{25}{16}} = \frac{\sqrt{25}}{\sqrt{16}} = \frac{5}{4}$) 
[beautiful math coming... please be patient] $\displaystyle x = \frac{5}{4}\ \ \text{or}\ \ x = \frac{5}{4}$  (expand the ‘plus or minus’ shorthand, if desired) 
[beautiful math coming... please be patient] $16x^2  25 = 0$  (original equation) 
[beautiful math coming... please be patient] $16x^2 = 25$  (add $\,25\,$ to both sides) 
[beautiful math coming... please be patient] $(4x)^2 = 25$  (rename lefthand side as a perfect square) 
[beautiful math coming... please be patient] $4x = \pm\sqrt{25}$  (use the theorem) 
[beautiful math coming... please be patient] $4x = \pm 5$  (rename: $\,\sqrt{25} = 5\,$) 
[beautiful math coming... please be patient] $\displaystyle x = \frac{\pm 5}{4}$  (divide both sides by $\,4\,$) 
[beautiful math coming... please be patient] $\displaystyle x = \frac{5}{4}\ \ \text{or}\ \ x = \frac{5}{4}$  (expand the ‘plus or minus’ shorthand, if desired) 
For more advanced students, a graph is displayed.
For example, the equation $\,x^2  9 = 0\,$
is optionally accompanied by the
graph of $\,y = x^2  9\,$ (the left side of the equation, dashed green)
and the graph of
$\,y = 0\,$ (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:
