Issolvi y/left(0.01(x-105)right)^2=z

$$\frac{ y }{ { \left(0.01(x-105) \right) }^{ 2 } } =z$$

Solvi għal y

$$y=\frac{z\left(x-105\right)^{2}}{10000}$$

$$x\neq 105$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Espandi \left(0.01\left(x-105\right)\right)^{2}.

$$\frac{y}{0.01^{2}\left(x-105\right)^{2}}=z$$

Ikkalkula 0.01 bil-power ta' 2 u tikseb 0.0001.

$$\frac{y}{0.0001\left(x-105\right)^{2}}=z$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-105\right)^{2}.

$$\frac{y}{0.0001\left(x^{2}-210x+11025\right)}=z$$

Uża l-propjetà distributtiva biex timmultiplika 0.0001 b'x^{2}-210x+11025.

$$\frac{y}{0.0001x^{2}-0.021x+1.1025}=z$$

L-ekwazzjoni hija f'forma standard.

$$\frac{1}{\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025}y=z$$

Iddividi ż-żewġ naħat b'\left(0.0001x^{2}-0.021x+1.1025\right)^{-1}.

$$\frac{\frac{1}{\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025}y\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}=\frac{z\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}$$

Meta tiddividi b'\left(0.0001x^{2}-0.021x+1.1025\right)^{-1} titneħħa l-multiplikazzjoni b'\left(0.0001x^{2}-0.021x+1.1025\right)^{-1}.

$$y=\frac{z\left(\frac{x^{2}}{10000}-\frac{21x}{1000}+1.1025\right)}{1}$$

Iddividi z b'\left(0.0001x^{2}-0.021x+1.1025\right)^{-1}.

$$y=\frac{z\left(x-105\right)^{2}}{10000}$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}\\x\neq 105\text{, }&\text{unconditionally}\\x=-100z^{-0.5}\sqrt{y}+105\text{; }x=100z^{-0.5}\sqrt{y}+105\text{, }&y\neq 0\text{ and }z\neq 0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}\\x\neq 105\text{, }&\text{unconditionally}\\x=-100\sqrt{\frac{y}{z}}+105\text{; }x=100\sqrt{\frac{y}{z}}+105\text{, }&z>0\text{ and }y>0\\x=-100\sqrt{\frac{y}{z}}+105\text{; }x=100\sqrt{\frac{y}{z}}+105\text{, }&z<0\text{ and }y<0\end{matrix}\right.$$