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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
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