Solving Quadratic Equations Using the Square Root
Property
Example
Solve using the Square Root Property: 5(w + 6)2 - 100 = 0
Solution
Step 1 Write the equation in the form x2
= a.
Add 100 to both sides.
Divide both sides by 5.
The equation
has the form
where x is w + 6 and a is 20. |
5(w + 6)2
(w + 6)2 |
= 100
= 20 |
Step 2 Use the Square Root Property. |
![](./articles_imgs/1225/solvin36.gif) |
![](./articles_imgs/1225/solvin37.gif) |
Step 3 Write each answer in simplified form. To solve for w, subtract 6 from
both sides. Simplify
![](./articles_imgs/1225/solvin38.gif) |
![](./articles_imgs/1225/solvin39.gif)
![](./articles_imgs/1225/solvin40.gif) |
![](./articles_imgs/1225/solvin41.gif)
![](./articles_imgs/1225/solvin42.gif) |
Step 4 Check each answer.
|
|
|
We leave the check to you.
So, the two solutions of 5(w + 6)2 - 100 = 0 are
![](./articles_imgs/1225/solvin43.gif)
Note:
Another way to write the solution is
![](./articles_imgs/1225/solvin44.gif)
|