Issolvi left(1-kright)x^2+x+1-k=0

$$\left( 1-k \right) { x }^{ 2 } +x+1-k = 0$$

Solvi għal k

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 1-k b'x^{2}.

$$x^{2}-kx^{2}+x+1-k=0$$

Naqqas x^{2} miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$-kx^{2}+x+1-k=-x^{2}$$

Naqqas x miż-żewġ naħat.

$$-kx^{2}+1-k=-x^{2}-x$$

Naqqas 1 miż-żewġ naħat.

$$-kx^{2}-k=-x^{2}-x-1$$

Ikkombina t-termini kollha li fihom k.

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

Iddividi ż-żewġ naħat b'-x^{2}-1.

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

Meta tiddividi b'-x^{2}-1 titneħħa l-multiplikazzjoni b'-x^{2}-1.

$$k=\frac{-x^{2}-x-1}{-x^{2}-1}$$

Iddividi -x^{2}-x-1 b'-x^{2}-1.

$$k=\frac{x^{2}+x+1}{x^{2}+1}$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{\sqrt{-\left(1-2k\right)\left(3-2k\right)}-1}{2\left(1-k\right)}\text{; }x=-\frac{\sqrt{-\left(1-2k\right)\left(3-2k\right)}+1}{2\left(1-k\right)}\text{, }&k\neq 1\text{ and }k\leq \frac{3}{2}\text{ and }k\geq \frac{1}{2}\\x=0\text{, }&k=1\end{matrix}\right.$$