Question

Formula general y comprobacion
2x²+x=55

Answer 1

$2x^2+x=55 \ \Rightarrow \ 2x^2+x-55=0 \\[2pt] \textbf{F\'ormula de la cuadr\'atica .}\\[2pt] ax^2+bx+c=0 \ \ \Rightarrow \ \ x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} \\[4pt] \text{En el ejercicio : }a=2 \ , \ b=1 \ , \ c=-55 \\[2pt] \text{reemplazando.} \\[4pt] x=\dfrac{-1\pm \sqrt{1^2-4(2)(-55)}}{2(2)}=\dfrac{-1\pm \sqrt{1+440}}{4}=\dfrac{-1\pm \sqrt{441}}{4} \\[2pt] x=\dfrac{-1\pm 21}{4}$

$\text{separando se obtienen las 2 soluciones }\\[4pt] x=\dfrac{-1+21}{4} \ \ \vee \ \ x=\dfrac{-1-21}{4} \\[4pt] x=5 \ \ \vee \ \ x=-\dfrac{11}{2} \\[4pt] \Rightarrow \ x=\left \{ -\dfrac{11}{2}\, , \, 5 \right \}$

$\textbf{Comprobaci\'on .} \\[4pt] \bullet \ x=-\dfrac{11}{2} \\[4pt] 2\left(-\dfrac{11}{2} \right)^2+\left(-\dfrac{11}{2} \right)=55 \\[4pt] 2\cdot \dfrac{121}{4}-\dfrac{11}{2}=55 \\[4pt] \dfrac{121}{2}-\dfrac{11}{2}=55 \\[4pt] \dfrac{110}{2}=55\\[4pt] 55=55 \ \ , \ verificado. \\[10pt] \bullet \ x=5 \\[4pt] 2(5^2)+5=55 \\[2pt] 2(25)+5=55 \\[2pt] 50+5=55 \\[2pt] 55=55 \ \ , \ verificado.$