x^2+b/ax+(b/2a)^2=-c/a+(b/2a)^2 eching

$$x ^ { 2 } + \frac { b } { a } x + ( \frac { b } { 2 a } ) ^ { 2 } = - \frac { c } { a } + ( \frac { b } { 2 a } ) ^ { 2 }$$

b uchun yechish (complex solution)

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini a ga ko'paytirish.

$$ax^{2}+bx+a\times \left(\frac{b}{2a}\right)^{2}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

\frac{b}{2a}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$ax^{2}+bx+a\times \frac{b^{2}}{\left(2a\right)^{2}}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

a\times \frac{b^{2}}{\left(2a\right)^{2}} ni yagona kasrga aylantiring.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

\frac{b}{2a}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+a\times \frac{b^{2}}{\left(2a\right)^{2}}$$

a\times \frac{b^{2}}{\left(2a\right)^{2}} ni yagona kasrga aylantiring.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

\left(2a\right)^{2} ni kengaytirish.

$$ax^{2}+bx+\frac{ab^{2}}{2^{2}a^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$ax^{2}+bx+\frac{ab^{2}}{4a^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

Surat va maxrajdagi ikkala a ni qisqartiring.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

\left(2a\right)^{2} ni kengaytirish.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{2^{2}a^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{4a^{2}}$$

Surat va maxrajdagi ikkala a ni qisqartiring.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{b^{2}}{4a}$$

Ikkala tarafdan \frac{b^{2}}{4a} ni ayirish.

$$ax^{2}+bx+\frac{b^{2}}{4a}-\frac{b^{2}}{4a}=-c$$

Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$ax^{2}\times 4a+bx\times 4a+b^{2}-b^{2}=-4ac$$

Shartlarni qayta saralash.

$$4aax^{2}+4abx+b^{2}-b^{2}=-4ac$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$4a^{2}x^{2}+4abx+b^{2}-b^{2}=-4ac$$

0 ni olish uchun b^{2} va -b^{2} ni birlashtirish.

$$4a^{2}x^{2}+4abx=-4ac$$

Ikkala tarafdan 4a^{2}x^{2} ni ayirish.

$$4abx=-4ac-4a^{2}x^{2}$$

Tenglama standart shaklda.

$$4axb=-4a^{2}x^{2}-4ac$$

Ikki tarafini 4ax ga bo‘ling.

$$\frac{4axb}{4ax}=-\frac{4a\left(ax^{2}+c\right)}{4ax}$$

4ax ga bo'lish 4ax ga ko'paytirishni bekor qiladi.

$$b=-\frac{4a\left(ax^{2}+c\right)}{4ax}$$

-4a\left(c+ax^{2}\right) ni 4ax ga bo'lish.

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

b uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini a ga ko'paytirish.

$$ax^{2}+bx+a\times \left(\frac{b}{2a}\right)^{2}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

\frac{b}{2a}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$ax^{2}+bx+a\times \frac{b^{2}}{\left(2a\right)^{2}}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

a\times \frac{b^{2}}{\left(2a\right)^{2}} ni yagona kasrga aylantiring.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+a\times \left(\frac{b}{2a}\right)^{2}$$

\frac{b}{2a}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+a\times \frac{b^{2}}{\left(2a\right)^{2}}$$

a\times \frac{b^{2}}{\left(2a\right)^{2}} ni yagona kasrga aylantiring.

$$ax^{2}+bx+\frac{ab^{2}}{\left(2a\right)^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

\left(2a\right)^{2} ni kengaytirish.

$$ax^{2}+bx+\frac{ab^{2}}{2^{2}a^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$ax^{2}+bx+\frac{ab^{2}}{4a^{2}}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

Surat va maxrajdagi ikkala a ni qisqartiring.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{\left(2a\right)^{2}}$$

\left(2a\right)^{2} ni kengaytirish.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{2^{2}a^{2}}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{ab^{2}}{4a^{2}}$$

Surat va maxrajdagi ikkala a ni qisqartiring.

$$ax^{2}+bx+\frac{b^{2}}{4a}=-c+\frac{b^{2}}{4a}$$

Ikkala tarafdan \frac{b^{2}}{4a} ni ayirish.

$$ax^{2}+bx+\frac{b^{2}}{4a}-\frac{b^{2}}{4a}=-c$$

Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$ax^{2}\times 4a+bx\times 4a+b^{2}-b^{2}=-4ac$$

Shartlarni qayta saralash.

$$4aax^{2}+4abx+b^{2}-b^{2}=-4ac$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$4a^{2}x^{2}+4abx+b^{2}-b^{2}=-4ac$$

0 ni olish uchun b^{2} va -b^{2} ni birlashtirish.

$$4a^{2}x^{2}+4abx=-4ac$$

Ikkala tarafdan 4a^{2}x^{2} ni ayirish.

$$4abx=-4ac-4a^{2}x^{2}$$

Tenglama standart shaklda.

$$4axb=-4a^{2}x^{2}-4ac$$

Ikki tarafini 4ax ga bo‘ling.

$$\frac{4axb}{4ax}=-\frac{4a\left(ax^{2}+c\right)}{4ax}$$

4ax ga bo'lish 4ax ga ko'paytirishni bekor qiladi.

$$b=-\frac{4a\left(ax^{2}+c\right)}{4ax}$$

-4a\left(c+ax^{2}\right) ni 4ax ga bo'lish.

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

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{bx+c}{x^{2}}\text{, }&\left(c\neq 0\text{ or }b\neq 0\right)\text{ and }\left(b=0\text{ or }x\neq -\frac{c}{b}\right)\text{ and }x\neq 0\text{ and }c\neq -bx\\a\neq 0\text{, }&c=0\text{ and }x=0\end{matrix}\right,$$