px^2+30x+25=0 eching

$$p x ^ { 2 } + 30 x + 25 = 0$$

p uchun yechish

$$p=-\frac{5\left(6x+5\right)}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 30x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$px^{2}+25=-30x$$

Ikkala tarafdan 25 ni ayirish.

$$px^{2}=-30x-25$$

Tenglama standart shaklda.

$$x^{2}p=-30x-25$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}p}{x^{2}}=\frac{-30x-25}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$p=\frac{-30x-25}{x^{2}}$$

-30x-25 ni x^{2} ga bo'lish.

$$p=-\frac{5\left(6x+5\right)}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{9-p}-3\right)}{p}\text{; }x=-\frac{5\left(\sqrt{9-p}+3\right)}{p}\text{, }&p\neq 0\\x=-\frac{5}{6}\text{, }&p=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{9-p}-3\right)}{p}\text{; }x=-\frac{5\left(\sqrt{9-p}+3\right)}{p}\text{, }&p\neq 0\text{ and }p\leq 9\\x=-\frac{5}{6}\text{, }&p=0\end{matrix}\right,$$