Issolvi 12=(1-3x)(1-3x)d+(1+3x)(1+3x)

$$12 = ( 1 - 3 x ) ( 1 - 3 x ) d + ( 1 + 3 x ) ( 1 + 3 x )$$

Solvi għal d

$$d=-\frac{9x^{2}+6x-11}{\left(1-3x\right)^{2}}$$

$$x\neq \frac{1}{3}$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika 1-3x u 1-3x biex tikseb \left(1-3x\right)^{2}.

$$12=\left(1-3x\right)^{2}d+\left(1+3x\right)\left(1+3x\right)$$

Immultiplika 1+3x u 1+3x biex tikseb \left(1+3x\right)^{2}.

$$12=\left(1-3x\right)^{2}d+\left(1+3x\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-3x\right)^{2}.

$$12=\left(1-6x+9x^{2}\right)d+\left(1+3x\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 1-6x+9x^{2} b'd.

$$12=d-6xd+9x^{2}d+\left(1+3x\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(1+3x\right)^{2}.

$$12=d-6xd+9x^{2}d+1+6x+9x^{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$d-6xd+9x^{2}d+1+6x+9x^{2}=12$$

Naqqas 1 miż-żewġ naħat.

$$d-6xd+9x^{2}d+6x+9x^{2}=12-1$$

Naqqas 1 minn 12 biex tikseb 11.

$$d-6xd+9x^{2}d+6x+9x^{2}=11$$

Naqqas 6x miż-żewġ naħat.

$$d-6xd+9x^{2}d+9x^{2}=11-6x$$

Naqqas 9x^{2} miż-żewġ naħat.

$$d-6xd+9x^{2}d=11-6x-9x^{2}$$

Ikkombina t-termini kollha li fihom d.

$$\left(1-6x+9x^{2}\right)d=11-6x-9x^{2}$$

L-ekwazzjoni hija f'forma standard.

$$\left(9x^{2}-6x+1\right)d=11-6x-9x^{2}$$

Iddividi ż-żewġ naħat b'1-6x+9x^{2}.

$$\frac{\left(9x^{2}-6x+1\right)d}{9x^{2}-6x+1}=\frac{11-6x-9x^{2}}{9x^{2}-6x+1}$$

Meta tiddividi b'1-6x+9x^{2} titneħħa l-multiplikazzjoni b'1-6x+9x^{2}.

$$d=\frac{11-6x-9x^{2}}{9x^{2}-6x+1}$$

Iddividi 11-6x-9x^{2} b'1-6x+9x^{2}.

$$d=\frac{11-6x-9x^{2}}{\left(3x-1\right)^{2}}$$

Solvi għal x (complex solution)

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

Solvi għal x

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