Question

Resolva as seguintes equações no método completando quadrados

A) 10x² + 7x + 1 = 0
B) 3x² - 2x - 1 = 0
C) x² + 3x - 10 = 0

Answer 1

A)

10x² + 7x + 1 = 0

x² + 7x/10 = -1/10

x² + 7x/10 + 49/400 = 9/400

(x + 7/20)² = 9/400

x + 7/20 = 3/20

x1 = -4/20 = -1/5

x + 7/20 = - 3/20

x2 = -10/20 = -1/2

B)

3x² - 2x - 1 = 0

x² - 2x/3 = 1/3

x² - 2x/3 + 1/9 = 4/9

(x - 1/3)² = 4/9

x - 1/3 = 2/3

x1 = 1/3 + 2/3 = 1

x - 1 = - 2/3

x2 = 1/3 - 2/3 = -1/3

C)

x² + 3x - 10 = 0

x² + 3x = 10

x² + 3x + 9/4 = 10 + 9/4

(x + 3/2)² = 49/4

x + 3/2 = 7/2

x1 = 7/2 - 3/2 = 4/2 = 2

x + 3/2 = -7/2

x2 = -7/2 - 3/2 = -10/2 = -5

Answer 2

Oi...

Resolução:

a)

10x² + 7x + 1 = 0

x² + 7x/10 = - 1/10

x² + 7x/10 + 49/400 = 9/400

(x + 7/20)² = 9/400

x + 7/20 = 3/20

x = 3/20 – 7/20

x’ = - 4/20 : 2

x’ = - 1/5

x + 7/20 = - 3/20

x = - 3/20 – 7/20

x” = - 10/20 : 10

x” = - 1/2

b)

3x² - 2x - 1 = 0

x² - 2x/3 = 1/3

x² - 2x/3 + 1/9 = 4/9

(x - 1/3)² = 4/9

x - 1/3 = 2/3

x’ = 1/3 + 2/3 = 1

x - 1 = - 2/3

x” = 1/3 - 2/3  

x” = -1/3

c)

x² + 3x - 10 = 0

x² + 3x = 10

x² + 3x + 9/4 = 10 + 9/4

(x + 3/2)² = 49/4

x + 3/2 = 7/2

x1 = 7/2 - 3/2  

x’ = 4/2

x’ = 2

x + 3/2 = - 7/2

x” = - 7/2 - 3/2

x” = -10/2

x” = - 5

Espero ter ajudado.