1+x^2-21x=050565 eching

$$1 + x ^ { 2 } - 21 x = 050565$$

x uchun yechish

$$x = \frac{\sqrt{437} + 21}{2} \approx 20,95227248$$

$$x=\frac{21-\sqrt{437}}{2}\approx 0,04772752$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 50565 ni ko'paytirish.

$$1+x^{2}-21x=0$$

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.

$$x^{2}-21x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -21 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4}}{2}$$

-21 kvadratini chiqarish.

$$x=\frac{-\left(-21\right)±\sqrt{441-4}}{2}$$

441 ni -4 ga qo'shish.

$$x=\frac{-\left(-21\right)±\sqrt{437}}{2}$$

-21 ning teskarisi 21 ga teng.

$$x=\frac{21±\sqrt{437}}{2}$$

x=\frac{21±\sqrt{437}}{2} tenglamasini yeching, bunda ± musbat. 21 ni \sqrt{437} ga qo'shish.

$$x=\frac{\sqrt{437}+21}{2}$$

x=\frac{21±\sqrt{437}}{2} tenglamasini yeching, bunda ± manfiy. 21 dan \sqrt{437} ni ayirish.

$$x=\frac{21-\sqrt{437}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{437}+21}{2} x=\frac{21-\sqrt{437}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 50565 ni ko'paytirish.

$$1+x^{2}-21x=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-21x=-1$$

-21 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{21}{2} olish uchun. Keyin, -\frac{21}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-21x+\left(-\frac{21}{2}\right)^{2}=-1+\left(-\frac{21}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{21}{2} kvadratini chiqarish.

$$x^{2}-21x+\frac{441}{4}=-1+\frac{441}{4}$$

-1 ni \frac{441}{4} ga qo'shish.

$$x^{2}-21x+\frac{441}{4}=\frac{437}{4}$$

x^{2}-21x+\frac{441}{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.

$$\left(x-\frac{21}{2}\right)^{2}=\frac{437}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{21}{2}\right)^{2}}=\sqrt{\frac{437}{4}}$$

Qisqartirish.

$$x-\frac{21}{2}=\frac{\sqrt{437}}{2} x-\frac{21}{2}=-\frac{\sqrt{437}}{2}$$

\frac{21}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{437}+21}{2} x=\frac{21-\sqrt{437}}{2}$$