12^2+x^2=x eching

$${ 12 }^{ 2 } + { x }^{ 2 } =x$$

x uchun yechish (complex solution)

$$x=\frac{1+5\sqrt{23}i}{2}\approx 0,5+11,989578808i$$

$$x=\frac{-5\sqrt{23}i+1}{2}\approx 0,5-11,989578808i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$144+x^{2}=x$$

Ikkala tarafdan x ni ayirish.

$$144+x^{2}-x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-x+144=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va 144 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 144}}{2}$$

-4 ni 144 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-576}}{2}$$

1 ni -576 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{-575}}{2}$$

-575 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±5\sqrt{23}i}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±5\sqrt{23}i}{2}$$

x=\frac{1±5\sqrt{23}i}{2} tenglamasini yeching, bunda ± musbat. 1 ni 5i\sqrt{23} ga qo'shish.

$$x=\frac{1+5\sqrt{23}i}{2}$$

x=\frac{1±5\sqrt{23}i}{2} tenglamasini yeching, bunda ± manfiy. 1 dan 5i\sqrt{23} ni ayirish.

$$x=\frac{-5\sqrt{23}i+1}{2}$$

Tenglama yechildi.

$$x=\frac{1+5\sqrt{23}i}{2} x=\frac{-5\sqrt{23}i+1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$144+x^{2}=x$$

Ikkala tarafdan x ni ayirish.

$$144+x^{2}-x=0$$

Ikkala tarafdan 144 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-x=-144$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-144+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=-144+\frac{1}{4}$$

-144 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=-\frac{575}{4}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{575}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{575}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{5\sqrt{23}i}{2} x-\frac{1}{2}=-\frac{5\sqrt{23}i}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1+5\sqrt{23}i}{2} x=\frac{-5\sqrt{23}i+1}{2}$$