Question

Resolva As equações do 2° Grau: a) 4x²-36=0 b) 7x²-21=0 c) x²-49=0 d) X.(x-3)=5x e) (x+1).(x-3)=-3 f) (x+5)²=25

Answer 1

a) 4x² - 36 = 0
4x² = 0 + 36
4x² = 36
x² = 36 / 4
x² = 9
x² - 9 = 0
x ( x - 9 ) = 0
x₁ = 0
x₂ = - 9

b) 7x² - 21 = 0 
7x² = 0 + 21
7x² = 21
x² = 21 / 7
x² = 3
x² - 3 = 0
x ( x - 3 ) = 0
x₁ = 0
x₂ = - 3

c) x² - 49 = 0
x ( x - 49 ) = 0
x₁ = 0
x₂ = - 49

d) x. ( x - 3 ) = 5x
x² - 3x = 5x
x² - 3x - 5x = 0
x² - 8x = 0
x (x - 8) = 0
x₁ = 0
x₂ = - 8

e) ( x + 1 ) . ( x - 3 ) = - 3
x² - 3x + x - 3 = - 3
x² - 2x - 3 + 3 = 0
x² - 2x = 0
x ( x - 2) = 0
x₁ = 0
x₂ = - 2

f) ( x + 5 )² = 25
x² + 10x + 25 = 25
x² + 10x + 25 - 25 = 0
x² + 10x = 0
x ( x + 10 ) = 0
x₁ = 0
x₂ = 10