Whakaoti i te P(x)=xP=80x-0.1x^2-(500+20x)

$$P ( x ) = x P = 80 x - 0.1 x ^ { 2 } - ( 500 + 20 x )$$

Whakaoti mō P

$$P=-\frac{x}{10}+60-\frac{500}{x}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Hei kimi i te tauaro o 500+20x, kimihia te tauaro o ia taurangi.

$$xP=80x-0.1x^{2}-500-20x$$

Pahekotia te 80x me -20x, ka 60x.

$$xP=60x-0.1x^{2}-500$$

He hanga arowhānui tō te whārite.

$$xP=-\frac{x^{2}}{10}+60x-500$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xP}{x}=\frac{-\frac{x^{2}}{10}+60x-500}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$P=\frac{-\frac{x^{2}}{10}+60x-500}{x}$$

Whakawehe 60x-\frac{x^{2}}{10}-500 ki te x.

$$P=-\frac{x}{10}+60-\frac{500}{x}$$

Whakaoti mō x (complex solution)

$$x=5\sqrt{P^{2}-120P+3400}-5P+300$$

$$x=-5\sqrt{P^{2}-120P+3400}-5P+300$$

Whakaoti mō x

$$x=5\sqrt{P^{2}-120P+3400}-5P+300$$

$$x=-5\sqrt{P^{2}-120P+3400}-5P+300\text{, }P\geq 10\sqrt{2}+60\text{ or }P\leq 60-10\sqrt{2}$$