1. Ex. 1 Solve by factoring. 2x2 + 9x + 7 = 0 6x2 – 3x = 0

2. Ex. 2 Solve by extracting square roots
A. 4x2 = 12
B. (x - 2)2 = 5
x2 = 3
Ex Completing the Square
x2 - 6x + 2 = 0
First, take 2 to the other side.
x2 - 6x = -2
To complete the square take half the x-term and square it. Add it to both sides.
x2 - 6x = -2
+ 9
+ 9
(x - 3)2 = 7

3. Ex. 4 Completing the Square when the leading coefficient is not 1
Divide each term by 3.
Take 5/3 to the other side.
Now, complete the square.
Take the square root of both sides.

4. Ex. 7 Use the Quadratic Formula to solve
x2 + 3x - 9 = 0

5. Ex. 8 Solve by factoring.
x4 - 3x2 + 2 = 0
Factor
Set both factors = 0
or factor again.
(x2 - 2)(x2 - 1) = 0
x2 - 2 = 0
x2 = 2
x2 - 1 = 0
x2 = 1

6. Ex. 9 Solve by grouping.
x3 - 3x2 - 3x + 9 = 0
x2(x - 3) - 3(x - 3) = 0
Factor out an (x - 3)
(x - 3)(x2 - 3) = 0
x = 3

7. Ex Solving a Radical
Isolate the radical.
Now square both sides.
2x + 7 = x2 + 4x + 4
0 = x2 + 2x - 3
Factor or use quad.
formula
0 = (x + 3)(x - 1)
Possible answers for x are - 3 and 1.
Check them in the original equation to see if
they work.
Only x = 1 works!

8. Ex. 11 An equation Involving Two Radicals
Isolate the more
complicated rad.
Square both sides.
Once again, isolate the radical.
Square both sides.
x2 + 2x + 1 = 4(x + 4)
(x - 5)(x + 3) = 0
x2 - 2x - 15 = 0
Only x = 5 works.

9. Ex. 12 Solving an Equation Involving
Absolute Value
Split into 2
equations.
x2 - 3x = -4x + 6
x2 - 3x = 4x -6
Now solve
them for x.
x2 + x - 6 = 0
x2 - 7x + 6 = 0
(x + 3)(x - 2) = 0
(x - 1)(x - 6) = 0
Possible answers are -3, 2, 1, and 6. Which ones work?
-3 and 1