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Solve the Quadratic
Contributed by: Jarvie
Solve using any method.

0, -2

0, 2

2

0

1/2, 0

4x2 - 8x = 0
Solve using any method.
x2 = 49

-7

7, -7

7

7√2

2√7

Solve using any method.

1/2, -3

2, -3

-1/2, -3

2x2 - 5x = 3

1/2, 3

-1/2, 3

Solve using any method.

-3 + 2√2

x2 + 6x = -1

± 2√2

-3 ± 2√2

-3 ± √8

3 ± √8

Solve using any method.

-7, -8

-8, 7

7, 8

x2 - 15x = -56

8, -7

± 8

When completing the square, what

number needs to be added to both sides?

-7

7

-49

49

14

x2 - 14x + 2 = 0

0

Solve using any method.

1

x2 + x = 0

0, 1

0, -1

1, -1

Solve using any method.

2/3, -5

2/3, 5

-5, -2/3

3x2 +13x = 10

-3, -10

3, -10

Solve using any method.

± √24

± 4√6

√24

x2 = 24

± 2√6

2√6

Solve using any method.

-√6

√6

No solution

-6

± √6

x2 + 6 = 0
Solve using any method.

1, 5

1, -5

-1, 5

-1, -5

No solution

x2 +4x - 5 = 0
Solve using any method.

No solution

-7 ± √37

7 ± √37

2
2
x2 + 7x - 3 = 0

-7 ± √61

7 ± √61

2
2
What is the next step when completing the square?
 Factor the left side, simplify the right

Take the square roots of both sides

Use the Zero Product Property

Set everything equal to zero

1.
2.
3.
4.
x2 + 4x + 4  = 32 + 4
x2 + 4x         = 32
x2 + 4x - 32 = 0

What is the measurement of each side of a square

with an area of 225 in2?

Area =

225 in2

15 in

± 15 in

√225

Say what?

Solve using any method.

0

-3

6x2 = 18x

0, 3

0, -3

3, -3

Solve using any method.

-2 ± 3√2

-2 + 3√2

x2 +4x - 14 = 0

No solution

2 ± 3√2

-2 ± √18

Solve using any method.

-1/3, 2

-1/3, -2

3x2 - 5x = 2

No solution

1/3, -2

1/3, 2

Solve using any method.
3x2- 18 = 0

√6

No solution

± 2√3

±6

±√6

Solve using any method.

9, 3

-3, -9

x2 + 6x - 27 = 0

-9, 3

-3, 9

9, -3

4. x + 6 = √24
3.  (x+6)2 = 24
5. x = -6 + √24
1. x2 + 12x = -12
2.  x2 + 12x + 36 = -12+36
6.  x = -6 + 2√6

In which step is the first mistake made?

x2 + 12x + 12 = 0

No mistake

Step 4

Step 3

Step 2

Distributive Property

Addition Property of Equality

Zero Product Property

Commutative Property of Multiplication

Which property justifies Step 2?
1.  (x+5)(x-3) = 0
x2 + 2x - 15 = 0
2.  x+5 = 0 or x -3 = 0
3.  x = -5, 3

x2 + 3x - 2 = 0

x2 - 3x + 2 = 0

x2 - 3x - 4 = 0

x2 - 3x - 2 = 0

Which quadratic equation is being used for

the following? (Quadratic Formula)

x =

3 ±√9 - 4(1)(-2)

2

x2 + 7x =-3

2x2 + 7x = -3

x2 + 7x - 4 = 0

2x2 - 7x + 3 = 0

Using the quadratic formula, which equation

is used?

x =
-7 ± √49 - 4(2)(3)
4

Fill in the blanks by dragging the correct choices

to their places.

x =
6
?
±
x2 - 6x = -8
36
?
-
(

2

4
?
)
(
1
?
)

(

8
?
)

Fill in the blanks of the quadratic formula by

dragging the boxes at the bottom into their

correct places.

x
=
-b
?
±

2a

?
b2
?
-
4ac
?
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