Question

Resolva usando o método de completar quadrados .

a ) x²+10×24=0

b ) x²-4y+3=0

c )x²+4x-12=0

d )x²-2x-3=0

Answer 1

Boa tarde

a )

x² + 10x + 24 = 0
x² + 10x = -24
x² + 10x + 25 = 25 - 24
(x + 5)² = 1
x + 5 = 1
x = -4
x = -6 

b )

x² - 4x + 3 = 0 
x² - 4x = -3
x² - 4x + 4 = 4 - 3
(x - 2)² = 1
x = 3
x = 1

c )

x² + 4x - 12 = 0
x² + 4x = 12
x² + 4x + 4 = 12 + 4
(x + 2)² = 16
x + 2 = 4
x = 2
x + 2 = -4
x = -6 

d)

x² - 2x - 3 = 0
x² - 2x = 3
x² - 2x + 1 = 3 + 1
(x - 1)² = 4

x = 3
x = -1