Réitigh ax^2=a+b-bx

$$a x ^ { 2 } = a + b - b x$$

Réitigh do a. (complex solution)

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain a ón dá thaobh.

$$ax^{2}-a=b-bx$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

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

Roinn an dá thaobh faoi x^{2}-1.

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

Má roinntear é faoi x^{2}-1 cuirtear an iolrúchán faoi x^{2}-1 ar ceal.

$$a=\frac{b-bx}{x^{2}-1}$$

Roinn b-bx faoi x^{2}-1.

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

Réitigh do b. (complex solution)

$$\left\{\begin{matrix}\\b=-a\left(x+1\right)\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$a+b-bx=ax^{2}$$

Bain a ón dá thaobh.

$$b-bx=ax^{2}-a$$

Comhcheangail na téarmaí ar fad ina bhfuil b.

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

Roinn an dá thaobh faoi 1-x.

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

Má roinntear é faoi 1-x cuirtear an iolrúchán faoi 1-x ar ceal.

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

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

$$b=-a\left(x+1\right)$$

Réitigh do a.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain a ón dá thaobh.

$$ax^{2}-a=b-bx$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

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

Roinn an dá thaobh faoi x^{2}-1.

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

Má roinntear é faoi x^{2}-1 cuirtear an iolrúchán faoi x^{2}-1 ar ceal.

$$a=\frac{b-bx}{x^{2}-1}$$

Roinn b-bx faoi x^{2}-1.

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

Réitigh do b.

$$\left\{\begin{matrix}\\b=-a\left(x+1\right)\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$a+b-bx=ax^{2}$$

Bain a ón dá thaobh.

$$b-bx=ax^{2}-a$$

Comhcheangail na téarmaí ar fad ina bhfuil b.

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

Roinn an dá thaobh faoi 1-x.

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

Má roinntear é faoi 1-x cuirtear an iolrúchán faoi 1-x ar ceal.

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

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

$$b=-a\left(x+1\right)$$