9x^2-6x+2=5x-6 eching

$$9 { x }^{ 2 } -6x+2=5x-6$$

x uchun yechish (complex solution)

$$x=\frac{11+\sqrt{167}i}{18}\approx 0,611111111+0,717935999i$$

$$x=\frac{-\sqrt{167}i+11}{18}\approx 0,611111111-0,717935999i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 5x ni ayirish.

$$9x^{2}-6x+2-5x=-6$$

-11x ni olish uchun -6x va -5x ni birlashtirish.

$$9x^{2}-11x+2=-6$$

6 ni ikki tarafga qo’shing.

$$9x^{2}-11x+2+6=0$$

8 olish uchun 2 va 6'ni qo'shing.

$$9x^{2}-11x+8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, -11 ni b va 8 ni c bilan almashtiring.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 9\times 8}}{2\times 9}$$

-11 kvadratini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 9\times 8}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121-36\times 8}}{2\times 9}$$

-36 ni 8 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121-288}}{2\times 9}$$

121 ni -288 ga qo'shish.

$$x=\frac{-\left(-11\right)±\sqrt{-167}}{2\times 9}$$

-167 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{167}i}{2\times 9}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±\sqrt{167}i}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{11±\sqrt{167}i}{18}$$

x=\frac{11±\sqrt{167}i}{18} tenglamasini yeching, bunda ± musbat. 11 ni i\sqrt{167} ga qo'shish.

$$x=\frac{11+\sqrt{167}i}{18}$$

x=\frac{11±\sqrt{167}i}{18} tenglamasini yeching, bunda ± manfiy. 11 dan i\sqrt{167} ni ayirish.

$$x=\frac{-\sqrt{167}i+11}{18}$$

Tenglama yechildi.

$$x=\frac{11+\sqrt{167}i}{18} x=\frac{-\sqrt{167}i+11}{18}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 5x ni ayirish.

$$9x^{2}-6x+2-5x=-6$$

-11x ni olish uchun -6x va -5x ni birlashtirish.

$$9x^{2}-11x+2=-6$$

Ikkala tarafdan 2 ni ayirish.

$$9x^{2}-11x=-6-2$$

-8 olish uchun -6 dan 2 ni ayirish.

$$9x^{2}-11x=-8$$

Ikki tarafini 9 ga bo‘ling.

$$\frac{9x^{2}-11x}{9}=-\frac{8}{9}$$

9 ga bo'lish 9 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{11}{9}x=-\frac{8}{9}$$

-\frac{11}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{18} olish uchun. Keyin, -\frac{11}{18} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{9}x+\left(-\frac{11}{18}\right)^{2}=-\frac{8}{9}+\left(-\frac{11}{18}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{18} kvadratini chiqarish.

$$x^{2}-\frac{11}{9}x+\frac{121}{324}=-\frac{8}{9}+\frac{121}{324}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{8}{9} ni \frac{121}{324} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{11}{9}x+\frac{121}{324}=-\frac{167}{324}$$

x^{2}-\frac{11}{9}x+\frac{121}{324} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{11}{18}\right)^{2}=-\frac{167}{324}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{18}\right)^{2}}=\sqrt{-\frac{167}{324}}$$

Qisqartirish.

$$x-\frac{11}{18}=\frac{\sqrt{167}i}{18} x-\frac{11}{18}=-\frac{\sqrt{167}i}{18}$$

\frac{11}{18} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{11+\sqrt{167}i}{18} x=\frac{-\sqrt{167}i+11}{18}$$