left(1--3/2right)x^2+x+1-k=0 eching

$$\left( 1- \frac{ -3 }{ 2 } \right) { x }^{ 2 } +x+1-k = 0$$

k uchun yechish

$$k=\frac{5x^{2}}{2}+x+1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{-3}{2} kasri manfiy belgini olib tashlash bilan -\frac{3}{2} sifatida qayta yozilishi mumkin.

$$\left(1-\left(-\frac{3}{2}\right)\right)x^{2}+x+1-k=0$$

-\frac{3}{2} ning teskarisi \frac{3}{2} ga teng.

$$\left(1+\frac{3}{2}\right)x^{2}+x+1-k=0$$

\frac{5}{2} olish uchun 1 va \frac{3}{2}'ni qo'shing.

$$\frac{5}{2}x^{2}+x+1-k=0$$

Ikkala tarafdan \frac{5}{2}x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x+1-k=-\frac{5}{2}x^{2}$$

Ikkala tarafdan x ni ayirish.

$$1-k=-\frac{5}{2}x^{2}-x$$

Ikkala tarafdan 1 ni ayirish.

$$-k=-\frac{5}{2}x^{2}-x-1$$

Tenglama standart shaklda.

$$-k=-\frac{5x^{2}}{2}-x-1$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-k}{-1}=\frac{-\frac{5x^{2}}{2}-x-1}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$k=\frac{-\frac{5x^{2}}{2}-x-1}{-1}$$

-\frac{5x^{2}}{2}-x-1 ni -1 ga bo'lish.

$$k=\frac{5x^{2}}{2}+x+1$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{10k-9}-1}{5}$$

$$x=\frac{-\sqrt{10k-9}-1}{5}$$

x uchun yechish

$$x=\frac{\sqrt{10k-9}-1}{5}$$

$$x=\frac{-\sqrt{10k-9}-1}{5}\text{, }k\geq \frac{9}{10}$$