Question

URGENTEEEEE!!!

escreva as equações do 2° grau abaixo na forma geral (ou em forma reduzida):

a) x. (x - 8) = 3x^2 - 4x

b) 25 = 2x^2 + 7x - 9 + x

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

d) (2x - 1)^2 = 2x + 1

e) (x + 4) . (x - 1) = 5x + 20

f) x^2 + 8x = + 12

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Answer 1

Resposta:

a) x. (x - 8) = 3x^2 - 4x

$x^{2} - 8x = 3x^{2} - 4x\\x^{2} - 8x - 3x^{2} + 4x = 0\\-2x^{2} - 4x = 0$

b) 25 = 2x^2 + 7x - 9 + x

$25 - 2x^{2} - 7x + 9 - x = 0\\34 - 2x^{2} - 8x = 0 : 2\\17 - x^{2} - 4x = 0\\-x^{2} - 4x + 17 = 0$

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

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

d) (2x - 1)^2 = 2x + 1

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

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) x^2 + 8x = + 12

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

Answer 2

Oie, tudo bom?

a)

$x \: . \: (x - 8) = 3x {}^{2} - 4x \\ x {}^{2} - 8x = 3x {}^{2} - 4x \\ x {}^{2} - 8x - 3x {}^{2} + 4x = 0 \\ \boxed{ - 2x {}^{2} + 4x = 0}$

b)

$25 = 2x {}^{2} + 7x - 9 + x \\ 25 = 2x {}^{2} + 8x - 9 \\ 25 - 2x {}^{2} - 8x + 9 = 0 \\ 34 - 2x {}^{2} - 8x = 0 \\ - 2x {}^{2} - 8x + 34 = 0 \\ \boxed{x {}^{2} + 14 - 17 = 0}$

c)

$18 + (x + 7) {}^{2} = 10x {}^{2} + 14x \\ 18 + x {}^{2} + 14x + 49 = 10x {}^{2} + 14x \\ 18 + x {}^{2} + 49 = 10x {}^{2} \\ 67 + x {}^{2} = 10x {}^{2} \\ 67 + x {}^{2} - 10x {}^{2} = 0 \\ 67 - 9x {}^{2} = 0 \\ \boxed{ - 9x {}^{2} + 67 = 0}$

d)

$(2x - 1) {}^{2} = 2x + 1 \\ 4x {}^{2} - 4x + 1 = 2x + 1 \\ 4x {}^{2} - 4x = 2x \\ 4x {}^{2} - 4x - 2x = 0 \\ \boxed{4x {}^{2} - 6x = 0 }$

e)

$(x + 4) \: . \: (x - 1) = 5x + 20 \\ x {}^{2} - x + 4x - 4 = 5x + 20 \\ x {}^{2} + 3x - 4 = 5x + 20 \\ x {}^{2} + 3x - 4 - 5x - 20 = 0 \\\boxed{x {}^{2} - 2x - 24 = 0 }$

f)

$x {}^{2} + 8x = 12 \\ \boxed{ x{}^{2} + 8x - 1 2= 0}$

Att. NLE Top Shotta