Question

2(x+1) (4x+1)-(2x+3)²=8​

Answer 1

Respuesta:

Aporte

2 (x + 1) (4 x + 1) - (2 x + 3)^2 = 8

Forma afirmativa

4 x^2 = 2 x + 15

16/61 (x - 1/4)^2 = 1

4 x^2 - 2 x - 15 = 0

4 x^2 - 2 x - 7 = 8

Soluciones

x = 1/4 -√61/4

x = 1/4 + √61/4

Answer 2

$\huge\color{red}\texttt{\colorbox{Res}{hola}$

$\boxed{\boxed{{\textsf{Tema:Ecuaciones cuadraticas}}}}$

$\huge\color{Black}\texttt{\colorbox{Res}{Problema}}$

$2(x+1)(4x+1)-(2x+3) ^ { 2 } =8$

$\huge\color{Gray}\texttt{\colorbox{Res}{Desarollo}}$

$2(x+1)(4x+1)-(2x+3) ^ { 2 } =8$

$\left(2x+2\right)\left(4x+1\right)-\left(2x+3\right)^{2}=8$

$8x^{2}+10x+2-\left(2x+3\right)^{2}=8$

$8x^{2}+10x+2-\left(4x^{2}+12x+9\right)=8$

$8x^{2}+10x+2-4x^{2}-12x-9=8$

$4x^{2}+10x+2-12x-9=8$

$4x^{2}-2x+2-9=8$

$4x^{2}-2x-7=8$

$4x^{2}-2x-7-8=0$

$4x^{2}-2x-15=0$

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

$x=\frac{-\left(-2\right)±\sqrt{4-16\left(-15\right)}}{2\times 4}$

$x=\frac{-\left(-2\right)±\sqrt{4+240}}{2\times 4}$

$x=\frac{-\left(-2\right)±\sqrt{244}}{2\times 4}$

$x=\frac{-\left(-2\right)±2\sqrt{61}}{2\times 4}$

$x=\frac{2±2\sqrt{61}}{2\times 4}$

$x=\frac{2±2\sqrt{61}}{8}$

$x=\frac{2\sqrt{61}+2}{8}$

$x=\frac{\sqrt{61}+1}{4}$

$x=\frac{2-2\sqrt{61}}{8}$

$x=\frac{1-\sqrt{61}}{4}$

$\huge\color{black}\texttt{\colorbox{Res}{Resultado final}}$

$x=\frac{\sqrt{61}+1}{4} \\ x=\frac{1-\sqrt{61}}{4}$

$\huge\color{blue}\texttt{\colorbox{Res}{彡Ｋａｋａｓｈｉ彡}}$