3x^2-211x+1800=0 eching

$$3 x ^ { 2 } - 211 x + 1800 = 0$$

x uchun yechish

$$x = \frac{\sqrt{22921} + 211}{6} \approx 60,399471593$$

$$x = \frac{211 - \sqrt{22921}}{6} \approx 9,93386174$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$3x^{2}-211x+1800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -211 ni b va 1800 ni c bilan almashtiring.

$$x=\frac{-\left(-211\right)±\sqrt{\left(-211\right)^{2}-4\times 3\times 1800}}{2\times 3}$$

-211 kvadratini chiqarish.

$$x=\frac{-\left(-211\right)±\sqrt{44521-4\times 3\times 1800}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-211\right)±\sqrt{44521-12\times 1800}}{2\times 3}$$

-12 ni 1800 marotabaga ko'paytirish.

$$x=\frac{-\left(-211\right)±\sqrt{44521-21600}}{2\times 3}$$

44521 ni -21600 ga qo'shish.

$$x=\frac{-\left(-211\right)±\sqrt{22921}}{2\times 3}$$

-211 ning teskarisi 211 ga teng.

$$x=\frac{211±\sqrt{22921}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{211±\sqrt{22921}}{6}$$

x=\frac{211±\sqrt{22921}}{6} tenglamasini yeching, bunda ± musbat. 211 ni \sqrt{22921} ga qo'shish.

$$x=\frac{\sqrt{22921}+211}{6}$$

x=\frac{211±\sqrt{22921}}{6} tenglamasini yeching, bunda ± manfiy. 211 dan \sqrt{22921} ni ayirish.

$$x=\frac{211-\sqrt{22921}}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{22921}+211}{6} x=\frac{211-\sqrt{22921}}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$3x^{2}-211x+1800=0$$

Tenglamaning ikkala tarafidan 1800 ni ayirish.

$$3x^{2}-211x+1800-1800=-1800$$

O‘zidan 1800 ayirilsa 0 qoladi.

$$3x^{2}-211x=-1800$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-211x}{3}=-\frac{1800}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{211}{3}x=-\frac{1800}{3}$$

-1800 ni 3 ga bo'lish.

$$x^{2}-\frac{211}{3}x=-600$$

-\frac{211}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{211}{6} olish uchun. Keyin, -\frac{211}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{211}{3}x+\left(-\frac{211}{6}\right)^{2}=-600+\left(-\frac{211}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{211}{6} kvadratini chiqarish.

$$x^{2}-\frac{211}{3}x+\frac{44521}{36}=-600+\frac{44521}{36}$$

-600 ni \frac{44521}{36} ga qo'shish.

$$x^{2}-\frac{211}{3}x+\frac{44521}{36}=\frac{22921}{36}$$

x^{2}-\frac{211}{3}x+\frac{44521}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{211}{6}\right)^{2}=\frac{22921}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{211}{6}\right)^{2}}=\sqrt{\frac{22921}{36}}$$

Qisqartirish.

$$x-\frac{211}{6}=\frac{\sqrt{22921}}{6} x-\frac{211}{6}=-\frac{\sqrt{22921}}{6}$$

\frac{211}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{22921}+211}{6} x=\frac{211-\sqrt{22921}}{6}$$