Solving Quadratic Equations Using the Square Root
Property
The Square Root Property can be used to solve a quadratic equation
written in the form x^{2} = a.
Property â€” Square Root Property
If x^{2} = a, then
Here, a is a nonnegative real number.
Examples
If x^{2} = 7, then
If (w + 6)^{2} = 3, then
Hereâ€™s how to use the Square Root Property to solve a quadratic equation.
Procedure â€”
To Solve a Quadratic Equation Using the Square Root Property
Step 1 Write the equation in the form x^{2} = a.
Step 2 Use the Square Root Property.
Step 3 Write each answer in simplified form.
Step 4 Check each answer.
Example 1
Solve using the Square Root Property: x^{2}  72 = 0
Solution
Step 1 Write the equation in the form x^{2}
= a.
Add 72 to both sides. 
x^{2}  72 x^{2} 
= 0 = 0 
Step 2 Use the Square Root Property. 


Step 3 Write each answer in simplified form. Simplify each square root. 


Step 4 Check each answer. 


So, the equation x^{2}  72 = 0 has two solutions,
and
.
Example 2
Solve using the Square Root Property: 4x^{2} + 64 = 0
Solution
Step 1 Write the equation in the form x^{2}
= a.
Subtract 64 from both sides.
Divide both sides by 4. 
4x^{2} + 64
4x^{2}
x^{2} 
= 0 = 64
= 16 
Step 2 Use the Square Root Property.



Step 3 Write each answer in simplified form.
Step 4 Check each answer.
We leave the check to you. 
x = 4 or 
x = 4 
So, the two solutions of 4x^{2} + 64 = 0 are 4 and 4.
Note:
Another way to write the solution is:
