Question

ME AJUDEM PELO AMOR DE DEUS!
a) X²+7x=0
b) -3x/2+9x=0
c)2x²+3x=0
d) (x+5)(x-1)=2x
e) (x+5)²=2x+23
f) (x-3)²=9
g (x+2)²=4

Answer 1

Olá Sofia,

dadas a equações do 2º grau, podemos resolver da seguinte forma:

$x^{2} +7x=0\\ x(x+7)=0\\\\ \begin{cases}x'=0\end{cases}\begin{cases}x+7=0\\ x''=-7\end{cases}\\\\\\ \boxed{S=\{0,-7\}}$

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$- \dfrac{3x^2}{2}+9x=0\\\\ x\left(- \dfrac{3}{2}x+9\right)=0\\\\\\ \begin{cases}x'=0\end{cases}\begin{cases}- \dfrac{3}{2}x+9=0\\\\ - \dfrac{3}{2}x=-9\\\\ - 3x=2*(-9)\\ -3x=-18\\\\ x= \dfrac{-18}{-3}\\\\ x''=6 \end{cases}\\\\\\ \boxed{S=\{0,6\}}$

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$2 x^{2} +3x=0\\ x(2x+3)=0\\\\ \begin{cases}x'=0\end{cases}\begin{cases}2x+3=0\\ 2x=-3\\ x''=- \dfrac{3}{2} \end{cases}\\\\\\ \boxed{S=\left\{0,- \dfrac{3}{2}\right\}}$

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$(x+5)(x-1)=2x\\ x^{2} -x+5x-5=2x\\ x^{2} +4x-2x-5=0\\ x^{2} +2x-5=0\\\\ \Delta=b^2-4ac\\ \Delta=2^2-4*1*(-5)\\ \Delta=4+20\\ \Delta=24\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2a}= \dfrac{-2\pm \sqrt{24} }{2*1}= -1\pm2 \sqrt{6}\\\\\\ \boxed{S=\{-1+2 \sqrt{6},~-1-2 \sqrt{6}\}}$

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$(x+5)^2=2x+23\\ (x+5)(x+5)=2x+23\\ x^{2} +5x+5x+25=2x+23\\ x^{2} +10x+25-2x-23=0\\ x^{2} +8x+2=0\\\\ \Delta=8^2-4*1*2\\ \Delta=64-8\\ \Delta=56\\\\\\ x= \dfrac{-8\pm \sqrt{56} }{2*1}=-4\pm2 \sqrt{14}\\\\\\ \boxed{S=\{-4+2 \sqrt{14},~-4-2 \sqrt{14}}$

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$(x-3)^2=9\\ (x-3)=\pm \sqrt{9}\\\\ (x-3)=\pm3~\to~\begin{cases}x-3=3~\to~x=3+3~\to~x'=6\\ x-3=-3~\to~x=-3+3~\to~x''=0\end{cases}\\\\\\ \boxed{S=\{0,6\}}$

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$(x+2)^2=4\\ (x+2)=\pm \sqrt{4}\\\\ x+2=\pm2~\to~\begin{cases}x+2=2~\to~x=2-2~\to~x'=0\\ x+2=-2~\to~x=-2-2~\to~x''=-4 \end{cases}\\\\\\ \boxed{S=\{0,-4\}}$

Espero ter ajudado e tenha ótimos estudos =))