Question

x2+11x=-24 resolver por formula general

ayuda instantánea porfa

Answer 1

La forma cuadrática :

ax² + bx + c.

x² + 11x + 24 = 0

Dónde  :

a = 1
b = 11
c = 24

Fórmula cuadrática.

 $\boxed{\boxed{ x_{1,2} = \frac{-b\ñ \sqrt{b^{2}-4ac}}{2a}}}$

Reemplazamos :

$x_{1,2} = \dfrac{-11\ñ \sqrt{(11)^{2}-4(1)(24)}}{2(1)} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{121-96}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{25}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ5}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ x_{1}= \dfrac{11+5}{2} = \dfrac{16}{2} = 8 \\ \\ \\ x_{2} = \dfrac{11-5}{2} = \dfrac{6}{2} = 3$

Solución :

8  y 3.

Answer 2

Resolvemos mediante la formula General:

$\boxed{\boxed{ \textbf{x = } \dfrac{\textbf{-b}\pm \sqrt{\textbf{b}^{\textbf{2}}\textbf{-4ac}}}{\textbf{2a}}}}$

Donde:

a= 1
b= 11
c= 24.

$x^{2} +11x=-24$
Movemos a todos los datos a la izquierda:

$x^{2} +11x+24=0$

Sustituimos datos y resolvemos:

$\textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{(11)}^{\textbf{2}}\textbf{-4(1)(24)}}}{\textbf{2(1)}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{121}\textbf{-96}}}{\textbf{2}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{25}}}{\textbf{2}} \\ \\ Resolvemos la ra\'iz cuadrada:$

$\textbf{x = } \dfrac{\textbf{-11}\pm\textbf{5}}{\textbf{2}} \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-11}+\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Primera ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-6}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{1} \textbf{ = -3}}}\checkmark\checkmark$

$\textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-11}-\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Segunda ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-16}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{2} \textbf{ = -8}}}\checkmark\checkmark$

Saludos y Suerte!!!!!