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Warm Up for Section 3.3
Factor:
(1). x2 – 49
(2). x2 + 6x – 16
(3). a2 – 7a + 12
(4). 6x2 + x – 15
(5). 3xa – 2xc + 6ay – 4yc
Answers for Warm Up for Section 3.3
Factor:
(1). x2 – 49 = (x + 7) (x – 7)
(2). x2 + 6x – 16 = (x + 8 )(x – 2)
(3). a2 – 7a + 12 = (a – 3)(a – 4)
(4). 6x2 + x – 15 = (3x + 5)(2x – 3)
(5). 3xa – 2xc + 6ay – 4yc = (x + 2y)(3a – 2c)
Solving Quadratic Equations by
Taking Square Roots
Section 3.3
Essential Question: How do I solve
quadratic equations by using square roots?
Rules for solving by taking the
square root:
1) Isolate the squared variable.
2) Take the square root of both sides.
3) Do not forget that you will usually have 2 answers!
Solve the equation by taking square roots:
(1). x2 – 5 = 0
x2 = 5
Add 5 to both sides
x= 5
Take square root of each side
Solution set:
  5
Solve the equation by taking square roots:
(2). 2x2 – 3 = 93
2x2 = 96
Add 3 to both sides
x2 = 48
Divide both sides by 2
x =  48
Take square root of each side
x = 4 3
Simplify radical
Solution set:
  4 3
Solve the equation by taking square roots:
(3). ½(y – 2)2 + 1 = 4
½(y – 2)2 = 3
(y – 2)2 = 6
(y – 2) =  6
y = 2 6
Solution set:
 2  6
Subtract 1 from both sides
Multiply both sides by 2
Take square root of each side
Add 2 to both side
Solve the equation by taking square roots:
(4). 2(y2 – 5) = -y2 – 1
2y2 – 10 = -y2 – 1
3y2 – 10 = – 1
3y2 = 9
Distribute
Add y2 to both sides
Add 10 to both sides
y2 = 3
Divide both sides by 3
y=  3
Take square root of both sides
Solution set:
 3
Try these with your partner:
(5).
x2 – 19 = 0

(7). 3(x –
19
5)2
(6). 5(x – 4)2 = 125

= 21
5  7 
(9). 3(x – 3)2 + 2 = 26
3  2 2 
 1, 9 
(8).
3 2
 x  2  5
5
 5 
10. The edge of a cube has the measure of (x + 5) units.
The surface area of the cube is 864 square units. What is
the measure of the edge of the cube?
6(x + 5)2 = SA
6(x + 5) 2 = 864
(x + 5) 2 = 144
x + 5 = ± 12
x = -5 ± 12
x = -17, 7
Edge = x + 5 = 7 + 5 = 12
12 units