SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

6𝑖

−𝟐 = −𝟑𝒊

SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

𝑥2 − 8𝑥 +−8

2

2

= −17 +−8

2

2

𝑥2 − 8𝑥 + 16 = −17 + 16

𝑥2 − 8𝑥 + 16 = −1

𝑥 − 4 2 = −1

𝑥2 − 8𝑥 = −17

𝑥 − 4 = ±𝑖

𝒙 = 𝟒 ± 𝒊

𝑥 − 4 2 = −1

SWBAT: Solve quadratic equations with complex roots.

Denominators: 𝒙: 𝒙 + 𝟏 𝑳𝑪𝑫 = x(x+1)

𝟒

𝒙∙

𝒙+𝟏

𝒙+𝟏 −

𝟑

(𝒙+𝟏)∙

𝒙

𝒙 =

7

1

4 𝑥+1 − 3𝑥

𝑥(𝑥+1) =

7

1

4𝑥+4 −3𝑥

𝑥(𝑥+1) =

7

1

𝑥+4

𝑥(𝑥+1) =

7

1∙

𝑥(𝑥+1)

𝑥(𝑥+1)

𝑥 + 4 = 7𝑥2 + 7𝑥

7𝑥2 + 6𝑥 − 4 = 0

x = − 𝟔 ± (𝟔)𝟐−𝟒(𝟕)(−𝟒)

𝟐(𝟕)

x = −𝟔 ± 𝟏𝟒𝟖

𝟏𝟒

x = −𝟔 ± 𝟒 𝟑𝟕

𝟏𝟒

x = −𝟔 ± 𝟐 𝟑𝟕

𝟏𝟒

x = −𝟑 ± 𝟑𝟕

𝟕

Divide by GCF of 2

SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

𝒙+𝟑

𝟑∙

𝒙

𝒙 +

𝒙+ 𝟑

𝒙∙

𝟑

𝟑 =

2

1∙

𝟑𝒙

𝟑𝒙

Denominators: 𝟑: 𝒙 𝑳𝑪𝑫 = 3x

𝑥 𝑥+3 + 3(𝑥+3)

3𝑥 =

6𝑥

3𝑥

𝑥2+3𝑥+3𝑥+9

3𝑥 =

6𝑥

3𝑥

𝑥2 + 6𝑥 + 9 = 6𝑥

𝑥2 + 9 = 0

𝒙𝟐 = −𝟗

𝒙 = ±𝟑𝒊

𝑥2 + 9 = 0

1.

SWBAT: Solve quadratic equations with complex roots.

4 ∙𝑥2

4 = 4(x – 2)

𝑥2 = 4𝑥 − 8

𝑥2 − 4𝑥 = −8

𝑥2 − 4𝑥 +−4

2

2

= −8 +−4

2

2

𝑥2 − 4𝑥 + 4 = −8 + 4

𝑥2 − 4𝑥 + 4 = −4

𝑥 − 2 2 = −4

𝑥 − 2 = ±2𝑖

𝒙 = 𝟐 ± 𝟐𝒊

𝑥 − 2 2 = −4

2.

SWBAT: Solve quadratic equations with complex roots.

2𝑥2 = -6x - 9

2𝑥2 + 6𝑥 + 9 = 0 x = − 𝟔 ± (𝟔)𝟐−𝟒(𝟐)(𝟗)

𝟐(𝟐)

x = −𝟔 ± −𝟑𝟔

𝟒

x = −𝟔 ± 𝟔𝒊

𝟒

x = −𝟑 ± 𝟑𝒊

𝟐

Divide by GCF of 2

3.

SWBAT: Solve quadratic equations with complex roots.

𝑥2 − 1𝑥 = 56

𝑥2 − 1𝑥 +−1

2

2

= 56 +−1

2

2

𝑥2 − 1𝑥 +1

4=

225

4

𝑥2 − 1𝑥 +1

4=

225

4

𝑥 −1

2

2

=225

4

𝑥 −1

2= ±

15

2

−𝟕, 𝟖

𝑥 −1

2

2

=225

4

𝑥 =1

2±

15

2

𝑥1 =1+15

2 = 8

𝑥2 =1−15

2 = -7

SWBAT: Solve quadratic equations with complex roots.

𝑥 + 8 = ±5

𝒙 = −𝟖 ± 𝟓

𝑥 + 8 2 = 25

−𝟏𝟑, −𝟑

𝑥1 = −8 + 5 = -3

𝑥2 = −8 − 5 = -13

5. (x + 8)2 = 25

SWBAT: Solve quadratic equations with complex roots.

(𝑥 + 3)(𝑥 + 4) = 5 ∙ 6

𝑥2 + 3𝑥 + 4𝑥 + 12 = 30

𝑥2 + 7𝑥 = 18

𝑥2 + 7𝑥 +7

2

2

= 18 +7

2

2

𝑥2 + 7𝑥 +49

4=

121

4

𝑥2 + 7𝑥 +49

4=

121

4

𝑥 +7

2

2

=121

4

𝑥 +7

2= ±

11

2

𝑥 =−7

2±

11

2

𝑥1 =−7+11

2 = 2

𝑥2 =−7−11

2 = -9

−𝟗, 𝟐

SWBAT: Solve quadratic equations with complex roots.

SWBAT: Solve quadratic equations with complex roots.

𝑥2 − 4𝑥 +−4

2

2

= −9 +−4

2

2

𝑥2 − 4𝑥 + 4 = −9 + 4

𝑥2 − 4𝑥 + 4 = −5

𝑥 − 2 2 = −5

𝑥2 − 4𝑥 = −9

𝑥 − 2 = ±𝑖 5

𝒙 = 𝟐 ± 𝒊 𝟓

𝑥 − 2 2 = −5