Quadratic Equations by Square Root Property 

The square root property is one method that can be used to solve quadratic equations.  This method is generally used on equations that have the form ax² = c   or   (ax + b)² = c, or an equation that can be re-expressed in either of those forms.    

To solve an equation by using the square root property, you will first isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable. Make sure to write the final answer in simplified form. 

Note that there is always the possibility of two roots for every square root: one positive and one negative.  Placing a  ± sign in front of the side containing the constant after you take the square root will ensure that the final answer will include both possible roots.


Example

Solve:  2x² + 3 = 27

Solution

First, isolate the portion of the equation that's actually being squared.

2x² + 3 − 3 = 27 − 3

2x² = 24

x² = 12

Now square root both sides and simplify.

 

Practice

Solve the following equations.

1.  x² − 15 = 34

2.  x² + 7 = 25

3.  3x² − 41 = 31

4.  (x + 3)² = 32

5.  2(x − 4)² = 90

Answers

1.  {−7, 7}

2. 

3. 

4. 

5.