Question

Determine o valor de x da equação:
$\begin{array}{|ccc|cc|}\sf 2 & 3 & -2 & 2 & 3\\0 & 1 & \sf x & 0 & 1\\2 &\sf x & -3 & 2 & \sf x\\\end{array} = 2$

Answer 1

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$\begin{vmatrix}\sf{2}&\sf{3}&\sf{-2}\\\sf{0}&\sf{1}&\sf{x}\\\sf{2}&\sf{x}&\sf{-3}\end{vmatrix}\begin{vmatrix}\sf{2}&\sf{3}\\\sf{0}&\sf{1}\\\sf{2}&\sf{x}\end{vmatrix}=\sf 2\\\sf -6-6x-0-0-2x^2+4=2\\\sf -2x^2-6x-6+4-2=0\\\sf -2x^2-6x-4=0\div(-2)\\\sf x^2+3x+2=0$

$\sf{\Delta=b^2-4ac}\\\sf{\Delta=3^2-4\cdot1\cdot2}\\\sf \Delta=9-8\\\sf \Delta=1\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-3\pm\sqrt{1}}{2\cdot1}\\\sf x=\dfrac{-3\pm1}{2}\begin{cases}\sf{x_1=\dfrac{-3+1}{2}=-\dfrac{2}{2}=-1}\\\sf{x_2=\dfrac{-3-1}{2}=-\dfrac{4}{2}=-2}\end{cases}$