Question

Como resolver (x+4)²=3(x+2)

Answer 1

Resposta:

(x + 4)²            = 3(x+2)

x² + 2.x.4 + 4² = 3.x + 3.2

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x²    +8x  + 16 = 3x  +  6

x² +8x -3x +16 -6 = 0

         \ /         \ /

x²     +5x      +10 = 0         onde a = 1        b = 5           c = 10

Δ = b² - 4.a.c

Δ = 5² - 4.1.10

Δ = 25 - 40

Δ = -15 .................. não existem raízes reais quando Δ for negativo

Explicação passo-a-passo:

Answer 2

OLÁ VAMOS A SUA PERGUNTA:⇒⇒

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$(x+4) ^ { 2 } =3(x+2)$

$x^{2}+8x+16=3\left(x+2\right)$

$x^{2}+8x+16=3x+6$

$x^{2}+8x+16=3x+6$

$x^{2}+8x+16-3x=6$

$x^{2}+5x+16=6$

$x^{2}+5x=6-16$

$x^{2}+5x=-10$

$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=-10+\left(\frac{5}{2}\right)^{2}$

$x^{2}+5x+\frac{25}{4}=-10+\frac{25}{4}$

$x^{2}+5x+\frac{25}{4}=-\frac{15}{4}$

$\left(x+\frac{5}{2}\right)^{2}=-\frac{15}{4}$

$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{-\frac{15}{4}}$

$x+\dfrac{5}{2}=\dfrac{\sqrt{15}i}{2} \\ x+\dfrac{5}{2}=-\dfrac{\sqrt{15}i}{2}$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese \:   x=\frac{-5+\sqrt{15}i}{2}\approx -2.5+1.936491673i}}}\ \checkmark \\ \boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese x=\frac{-\sqrt{15}i-5}{2}\approx -2.5-1.936491673i}}}\ \checkmark$

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