Réitigh 2x^2+cx^2+7x+60=0

$$2 x ^ { 2 } + c x ^ { 2 } + 7 x + 60 = 0$$

Réitigh do c.

$$c=-2-\frac{7}{x}-\frac{60}{x^{2}}$$

$$x\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 2x^{2} ón dá thaobh. Is ionann rud ar bith a dhealaítear ó nialas agus a shéanadh.

$$cx^{2}+7x+60=-2x^{2}$$

Bain 7x ón dá thaobh.

$$cx^{2}+60=-2x^{2}-7x$$

Bain 60 ón dá thaobh.

$$cx^{2}=-2x^{2}-7x-60$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$x^{2}c=-2x^{2}-7x-60$$

Roinn an dá thaobh faoi x^{2}.

$$\frac{x^{2}c}{x^{2}}=\frac{-2x^{2}-7x-60}{x^{2}}$$

Má roinntear é faoi x^{2} cuirtear an iolrúchán faoi x^{2} ar ceal.

$$c=\frac{-2x^{2}-7x-60}{x^{2}}$$

Roinn -2x^{2}-7x-60 faoi x^{2}.

$$c=-2-\frac{7x+60}{x^{2}}$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\text{ and }c\leq -\frac{431}{240}\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right.$$