The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 5.21: SOLVING QUADRATIC EQUATIONS

BY FINDING SQUARE ROOTS

-------------------------------------------------------------------------------------

Follow the steps below to solve a quadratic equation of the formax^2 +c= 0 , whereacannot

equal 0:

1. Isolate the squared term on one side of the equation.


2. Find the square root of the terms on both sides of the equation. Remember the
   following:
   
   
   • All positive numbers have two square roots. One is positive; the other is negative.
   
   
   • The square root of 0 is 0.
   
   
   • All negative numbers have no real square roots.
   
   
   
   


3. Substitute your solution, if there is one, in the original equation to check your work.

EXAMPLE

Solve 2 x^2 − 50 = 0.

To isolatex^2 , add 50 to both sides of the equation, then divide by 2. The equivalent equation is

x^2 = 25.

Find the square root of each side.

√

x^2 =±

√

25 .x=5;x=− 5

Check:2(5)^2 − 50 = 0 and2(−5)^2 − 50 = 0

DIRECTIONS: Solve. If there are no real solutions, write ‘‘no real solutions.’’

1. x^2 = 121 2. 4 x^2 = 400


2. x^2 − 1 = 0 4. 3 x^2 = 0


3. x^2 + 49 = 0 6. − 4 x^2 + 196 = 0


4. x^2 + 49 = 49 8. − 5 x^2 − 20 = 0

CHALLENGE:Deanna solvedx^2 + 16 =0bywritingx^2 =16. She then found

the square root of both sides of the equation and found thatx=4and

x=−4. She substituted both of these values inx^2 =16 and both answers

checked. But her teacher told her that there are no real solutions to the

original equation. What was Deanna’s mistake?

217

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.