Issolvi k(x-1)^2+2=kx-k+2

$$k ( x - 1 ) ^ { 2 } + 2 = k x - k + 2$$

Solvi għal k (complex solution)

$$\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=1\text{ or }x=2\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

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

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

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

Naqqas kx miż-żewġ naħat.

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

Ikkombina -2kx u -kx biex tikseb -3kx.

$$kx^{2}-3kx+k+2=-k+2$$

Żid k maż-żewġ naħat.

$$kx^{2}-3kx+k+2+k=2$$

Ikkombina k u k biex tikseb 2k.

$$kx^{2}-3kx+2k+2=2$$

Naqqas 2 miż-żewġ naħat.

$$kx^{2}-3kx+2k=2-2$$

Naqqas 2 minn 2 biex tikseb 0.

$$kx^{2}-3kx+2k=0$$

Ikkombina t-termini kollha li fihom k.

$$\left(x^{2}-3x+2\right)k=0$$

Iddividi 0 b'x^{2}-3x+2.

$$k=0$$

Solvi għal k

$$\left\{\begin{matrix}\\k=0\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=1\text{ or }x=2\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

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

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

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

Naqqas kx miż-żewġ naħat.

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

Ikkombina -2kx u -kx biex tikseb -3kx.

$$kx^{2}-3kx+k+2=-k+2$$

Żid k maż-żewġ naħat.

$$kx^{2}-3kx+k+2+k=2$$

Ikkombina k u k biex tikseb 2k.

$$kx^{2}-3kx+2k+2=2$$

Naqqas 2 miż-żewġ naħat.

$$kx^{2}-3kx+2k=2-2$$

Naqqas 2 minn 2 biex tikseb 0.

$$kx^{2}-3kx+2k=0$$

Ikkombina t-termini kollha li fihom k.

$$\left(x^{2}-3x+2\right)k=0$$

Iddividi 0 b'x^{2}-3x+2.

$$k=0$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&k=0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}\\x=1\text{; }x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=0\end{matrix}\right.$$