Question

(x+5) x (x-2) + 3x-7=4x equação poliminial

Answer 1

Resposta:

$x=3\sqrt{2}-1$ ou $x=-3\sqrt{2}-1$

Explicação passo a passo:

$(x+5)*(x-2)+3x-7=4x \\ x*x+x*(-2)+5*x+5*(-2)+3x-7=4x \\ x^2-2x+5x-10+3x-7=4x \\ x^2-2x+5x+3x-4x-10-7=0 \\ x^2+2x-17=0$

a = 1 // b = 2 // c = -17

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a} \\\\ x=\frac{-2\±\sqrt{2^2-4*1*(-17)}}{2*1} \\\\ x=\frac{-2\±\sqrt{4+68}}{2} \\\\ x=\frac{-2\±\sqrt{72}}{2} \\\\ x=\frac{-2\±6\sqrt{2}}{2}$

Quando ± for +:

$x=\frac{-2+6\sqrt{2}}{2}=\frac{6\sqrt{2}-2}{2}=3\sqrt{2}-1$

Quando ± for -:

$x=\frac{-2-6\sqrt{2}}{2}=\frac{-6\sqrt{2}-2}{2}=-3\sqrt{2}-1$