Question

Resuelve
la ecuación (3x²+ 2x(4+2x)+1=20-2x(2-x)​

Answer 1

Respuesta:

$\left \{ {{x=-8+\sqrt{83} } \atop {x=-8-\sqrt{83} }} \right.$

Explicación paso a paso:

$(3x^{2} + 8x+ 4x +1 = 20 - 4x + 2x^{2} )\\3x^{2} +8x+4x+4x-2x^{2} =20-1\\x^{2}+16x=19\\x^{2}+16x-19=0$

Factorizando

$x=\frac{-16+-\sqrt{16^{2} -4(1)(-19)} }{2(1)}\\ x=\frac{-16+-\sqrt{256+76} }{2}\\ x=\frac{-16+-\sqrt{332} }{2}\\ x=\frac{-16+-2\sqrt{83} }{2} \\x=\frac{2(-8+-\sqrt{83}) }{2}$$\left \{ {{x=-8+\sqrt{83} } \atop {x=-8-\sqrt{83} }} \right.$