Question

Resolva as equações pelo método de áreas complementando o quadrado:

a) x²+4x=12





b) x²+6x-27=0




c)x²+12x-28=0




d)x²+8x=9

Answer 1

Olá, tudo bem?

$\text{a)}~x^{2} + 4x = 12~(+4)\rightarrow x^{2} + 4x + 4 = 16\rightarrow\\\\(x + 2)^{2} = 16\rightarrow x + 2 = \pm \sqrt{16}\rightarrow x + 2 = \pm 4\\\\\boxed{x_{1}=-6}~~\text{ou}~~\boxed{x_{2}=2}$

$\text{b)}~x^{2} + 6x - 27 = 0~(+36)\rightarrow x^{2} + 6x + 9 = 36\rightarrow\\\\(x + 3)^{2}=36\rightarrow x + 3 = \pm \sqrt{36}\rightarrow x + 3 = \pm 6\\\\\boxed{x_{1}=-9}~~\text{ou}~~\boxed{x_{2}=3}$

$\text{c)}~x^{2} + 12x - 28 = 0~(+64)\rightarrow x^{2} + 12x + 36 = 64\rightarrow\\\\(x + 6)^{2} = 64\rightarrow x + 6 = \pm \sqrt{64}\rightarrow x + 6 = \pm 8\\\\\boxed{x_{1}=-14}~~\text{ou}~~\boxed{x_{2}=2}$

$\text{d)}~x^{2} + 8x = 9~(+16)\rightarrow x^{2} + 8x + 16 = 25\rightarrow\\\\(x + 4)^{2} = 25\rightarrow x + 4 = \pm \sqrt{25}\rightarrow x + 4 = \pm 5\\\\\boxed{x_{1}=-9}~~\text{ou}~~\boxed{x_{2}=1}$

Qualquer dúvida, por favor, é só me comunicar, ok?