Question

resolva as equacoea pelo metodo de completar quadrado

a)x2-6x=16
b)t2-20t=44
c)y2-8y+8=17
d)x2+10x+18=29

Answer 1

Olá Junior

a) 

x² - 6x = 16

x² - 6x + 9 = 16 + 9

(x - 3)² = 25

x - 3 = 5
x = 8

x - 3 = -5
x = -2

b)

t² - 20t = 44

t² - 20t + 100 = 44 + 100

(t - 10)² = 144

t - 10 = 12
t = 22

t - 10 = -12
t = -2 

c)

y² - 8y + 8 = 17 

y² - 8y + 16 + 8 = 17 + 16

y² - 8y + 16 = 25

(y - 4)² = 25

y - 4 = 5
y = 9

y - 4 = -5
y = -1

d)

x² + 10x = 11

x² + 10x + 25 = 11 + 25

(x + 5)² = 36

x + 5 = 6
x = 1

x + 5 = -6
x = -11