Question

1) Escreva as equações do 2o grau abaixo na forma geral (ou forma reduzida):
a) x.(x – 8) = 3x2 – 4x
b) 25 = 2x2 + 7x – 9 + x
c) 18 + (x + 7)2 = 10x2 + 14x
d) (2x – 1)2 = 2x + 1
e) (x + 4).(x – 1) = 5x +20
f) x2 + 8x = +12

Answer 1

Resposta:

a) x.(x – 8) = 3x2 – 4x

${x}^{2} - 8x = {3x}^{2} - 4x \\ {x }^{2} - 8x - {3x}^{2} + 4x = 0 \\ - {2x}^{2} - 4x = 0 \times ( - 1) \\ {2x}^{2} + 4x = 0$

b) 25 = 2x2 + 7x – 9 + x

$25 - {2x}^{2} - 7x + 9 - x = 0 \\ - {2x}^{2} - 8x + 34 = 0$

c) 18 + (x + 7)2 = 10x2 + 14x

$18 + {x}^{2} + 14x + 49 - {10x}^{2} - 14x = 0 \\ - {9x}^{2} + 67 = 0 \times ( - 1) \\ {9x}^{2} - 67 = 0$

d) (2x – 1)2 = 2x + 1

${4x}^{2} - 4x - 2x - 1 = 0 \\ {4x}^{2} - 6x - 1 = 0$

e) (x + 4).(x – 1) = 5x +20

${x}^{2} - x + 4x - 4 = 5x + 20 \\ {x}^{2} + 3x - 4 - 5x - 20 = 0 \\ {x}^{2} - 2x - 24 = 0$

f) x2 + 8x = +12

${x}^{2} + 8x - 12 = 0$