1/2x^2+bx+c=0 eching

$$\frac { 1 } { 2 } x ^ { 2 } + b x + c = 0$$

b uchun yechish (complex solution)

$$\left\{\begin{matrix}b=-\frac{x}{2}-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{2}x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$bx+c=-\frac{1}{2}x^{2}$$

Ikkala tarafdan c ni ayirish.

$$bx=-\frac{1}{2}x^{2}-c$$

Tenglama standart shaklda.

$$xb=-\frac{x^{2}}{2}-c$$

Ikki tarafini x ga bo‘ling.

$$\frac{xb}{x}=\frac{-\frac{x^{2}}{2}-c}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$b=\frac{-\frac{x^{2}}{2}-c}{x}$$

-\frac{x^{2}}{2}-c ni x ga bo'lish.

$$b=-\frac{x}{2}-\frac{c}{x}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{x}{2}-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{2}x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$bx+c=-\frac{1}{2}x^{2}$$

Ikkala tarafdan c ni ayirish.

$$bx=-\frac{1}{2}x^{2}-c$$

Tenglama standart shaklda.

$$xb=-\frac{x^{2}}{2}-c$$

Ikki tarafini x ga bo‘ling.

$$\frac{xb}{x}=\frac{-\frac{x^{2}}{2}-c}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$b=\frac{-\frac{x^{2}}{2}-c}{x}$$

-\frac{x^{2}}{2}-c ni x ga bo'lish.

$$b=-\frac{x}{2}-\frac{c}{x}$$

c uchun yechish

$$c=-\frac{x\left(x+2b\right)}{2}$$

Yechim qadamlari

Ikkala tarafdan \frac{1}{2}x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$bx+c=-\frac{1}{2}x^{2}$$

Ikkala tarafdan bx ni ayirish.

$$c=-\frac{1}{2}x^{2}-bx$$