2x^2+cx^2+7x+60=0 eching

$$2 x ^ { 2 } + c x ^ { 2 } + 7 x + 60 = 0$$

c uchun yechish

$$c=-2-\frac{7}{x}-\frac{60}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$cx^{2}+7x+60=-2x^{2}$$

Ikkala tarafdan 7x ni ayirish.

$$cx^{2}+60=-2x^{2}-7x$$

Ikkala tarafdan 60 ni ayirish.

$$cx^{2}=-2x^{2}-7x-60$$

Tenglama standart shaklda.

$$x^{2}c=-2x^{2}-7x-60$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}c}{x^{2}}=\frac{-2x^{2}-7x-60}{x^{2}}$$

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

$$c=\frac{-2x^{2}-7x-60}{x^{2}}$$

-2x^{2}-7x-60 ni x^{2} ga bo'lish.

$$c=-2-\frac{7x+60}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{-240c-431}-7}{2\left(c+2\right)}\text{; }x=-\frac{\sqrt{-240c-431}+7}{2\left(c+2\right)}\text{, }&c\neq -2\text{ and }c\leq -\frac{431}{240}\\x=-\frac{60}{7}\text{, }&c=-2\end{matrix}\right,$$