This document introduces the square root property and method for solving quadratic equations using square roots. It provides 3 steps: 1) isolate the term being squared, 2) take the square root of both sides, and 3) solve the remaining equation if needed. Examples are shown of solving equations of the form x^2=a, (x-b)^2=c, and (ax-b)^2=c by taking the square root and solving the resulting linear equations. It is noted that some quadratic equations using this method may have no real solutions.

1. Chapter 16.1 p. 563
Solving Quadratic
Equations by the Square
Root Property

2. Square Root Property
We will be using factoring to solve quadratic
equations in this chapter as well.
This chapter will introduce additional
methods for solving quadratic equations.
Square Root Property
If b is a real number and a2
= b, then
ba ±=

3. STEPS TO SOLVE QUADRATICS
WITH SQUARE ROOTS
1. Isolate what is being squared on one side of the
equation EX: 2x2
+ 2 = 4
-2 -2
2x2
= 2
÷2 ÷2
x2
= 1
2. Take a square root of each side. √ x2
= √1
x = ± 1
3. Solve the remaining equation for x (if needed)

4. Solve x2
= 49
2±=x
Solve (y – 3)2
= 4
Solve 2x2
= 4
x2
= 2
749 ±=±=x
TWO OPTIONS:
y – 3 = + 2 or y – 3 = - 2
y = 5 or y = 1
243 ±=±=−y
Square Root Property
Example

5. Solve x2
+ 4 = 0
x2
= −4
There is no real solution because the square root
of −4 is not a real number.
Square Root Property
Example

6. Solve (x + 2)2
= 25
x = −2 ± 5
x = −2 + 5 or x = −2 – 5
x = 3 or x = −7
5252 ±=±=+x
Square Root Property
Example

7. Solve (3x – 17)2
= 28
72173 ±=x
3
7217 ±
=x
727428 ±=±=±3x – 17 =
Square Root Property
Example