Welcome To Leore’s Tutorial!
I
will help you Solve Quadratic Equations by Finding Square Roots (section
5.2)
·
These are the basic equations:
= 
and
= 
Quotient
Property and Product
Property
·
Here are the ways to actually solve them:
Example
#1
Simplify 
Step 1:
Rewrite original problem. 
Step 2:
Find the factors of 24
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2 |
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12 |
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3 |
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8 |
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4 |
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6 |
Step 3:
Find the number that has a square root that is a whole number.
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I chose the 
because 
2, then use the pair
later to separate the original square root
Step 4:
Break up the original square root using the Product Property.
= 
Step 5:
Simplify. 2
The Final Answer is 2
Example
#2
Simplify
Step
1: Using the Quotient Property, separate!
=
Step
2: Search for the number that is a
whole number square root.
6 (because 6
= 36)
Step 3:
Simplify. 
The Final Answer is 
Example
#3
Simplify
Step
1: Separate the radical into two parts
using quotient property.
=
Step 2: Multiply the new radical
by 
so they two square root signs cancel out and
then multiply. The two square roots cancel out.
× 
= 
Step 3: You
thought you were done right? Well hold on! 
can be simplified even
further! So start by finding the factors of.
|
2 |
|
60 |
|
3 |
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40 |
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4 |
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30 |
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5 |
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24 |
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6 |
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20 |
Step 4: Search
for a number that has a whole number square root.
|
2 |
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60 |
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3 |
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40 |
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30 |
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5 |
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24 |
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6 |
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20 |
I chose the because 2, then use the pair later to separate the
original square root
Step 5: 
into the two parts that you picked.
Step 6:
Simplify the new square roots.
2
Step 7:
Add the two parts together.
The Final Answer is 
Example #4
Solve 3x2-8=16
Step 1: Move all the numbers to one side.
3x2-8=16
+8 +8
3x2=24
Step 2: Divide
both sides by 3 so that the x2 will be alone.
=
x2 = 8
Step 3: Take
the square root of x2 and 8 so that the x2 will cancel
out.
= 
Step 4: Since
cancels out, write out what is left.
X=
Step 5:
Because a square root can be either positive or negative, the answer has to be…
X=±
The final answer is X=±
Example #5
Solve 
(x+6)2=12
Step 1: Multiply each side by 2 to cancel out the
.
2
(x+6)2 = 12
=
(x+6)2 = 24
Step 2:
Take the square roots from each side and cancel out the square root and the
squared sign.
= 
Step 3:
Rewrite the problem.
x+6= 
Step 4:
Take 6 away from both sides.
x+6=
-6 -6
I added
the 
because it can be either
= positive
or negative.
X= -6
Step 5:
But wait! You can simplify 
!
= 
Step 6:
Simplify further.
= 2
Step 7:
Add the two together!
X= -6
Step 8: Find
out the two solutions.
X= -6
or -6+2
The final answer is X= -6
or
-6+2
I HOPE YOU LEARNED HOW TO SOLVE QUADRATIC EQUATIONS BY
FINDING SQUARE ROOTS!
Try some of the problems below!
1.
2.
3. 4x2-18=2
4. 
(x-3)2=14
5. 
6. 2x2+8=16
The answers are on the
solution page!