Réitigh -x^2-ax^2+ax+2x-1=0

$$- x ^ { 2 } - a x ^ { 2 } + a x + 2 x - 1 = 0$$

Réitigh do a. (complex solution)

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

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

$$-x^{2}-ax^{2}+ax-1=-2x$$

Cuir 1 leis an dá thaobh.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Cuir x^{2} leis an dá thaobh.

$$-ax^{2}+ax=-2x+1+x^{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

$$\left(-x^{2}+x\right)a=-2x+1+x^{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x-x^{2}\right)a=x^{2}-2x+1$$

Roinn an dá thaobh faoi -x^{2}+x.

$$\frac{\left(x-x^{2}\right)a}{x-x^{2}}=\frac{\left(x-1\right)^{2}}{x-x^{2}}$$

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

$$a=\frac{\left(x-1\right)^{2}}{x-x^{2}}$$

Roinn \left(x-1\right)^{2} faoi -x^{2}+x.

$$a=-1+\frac{1}{x}$$

Réitigh do a.

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

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

$$-x^{2}-ax^{2}+ax-1=-2x$$

Cuir 1 leis an dá thaobh.

$$-x^{2}-ax^{2}+ax=-2x+1$$

Cuir x^{2} leis an dá thaobh.

$$-ax^{2}+ax=-2x+1+x^{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

$$\left(-x^{2}+x\right)a=-2x+1+x^{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(x-x^{2}\right)a=x^{2}-2x+1$$

Roinn an dá thaobh faoi -x^{2}+x.

$$\frac{\left(x-x^{2}\right)a}{x-x^{2}}=\frac{\left(x-1\right)^{2}}{x-x^{2}}$$

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

$$a=\frac{\left(x-1\right)^{2}}{x-x^{2}}$$

Roinn \left(x-1\right)^{2} faoi -x^{2}+x.

$$a=-1+\frac{1}{x}$$

Réitigh do x.

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=\frac{1}{a+1}\text{, }&a\neq -1\end{matrix}\right.$$