x^2-x=120/7 eching

$$x ^ { 2 } - x = \frac { 120 } { 7 }$$

x uchun yechish

$$x=\frac{\sqrt{3409}}{14}+\frac{1}{2}\approx 4,670474451$$

$$x=-\frac{\sqrt{3409}}{14}+\frac{1}{2}\approx -3,670474451$$

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.

$$x^{2}-x=\frac{120}{7}$$

Tenglamaning ikkala tarafidan \frac{120}{7} ni ayirish.

$$x^{2}-x-\frac{120}{7}=\frac{120}{7}-\frac{120}{7}$$

O‘zidan \frac{120}{7} ayirilsa 0 qoladi.

$$x^{2}-x-\frac{120}{7}=0$$

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 -\frac{120}{7} ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-\frac{120}{7}\right)}}{2}$$

-4 ni -\frac{120}{7} marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+\frac{480}{7}}}{2}$$

1 ni \frac{480}{7} ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{\frac{487}{7}}}{2}$$

\frac{487}{7} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±\frac{\sqrt{3409}}{7}}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\frac{\sqrt{3409}}{7}}{2}$$

x=\frac{1±\frac{\sqrt{3409}}{7}}{2} tenglamasini yeching, bunda ± musbat. 1 ni \frac{\sqrt{3409}}{7} ga qo'shish.

$$x=\frac{\frac{\sqrt{3409}}{7}+1}{2}$$

1+\frac{\sqrt{3409}}{7} ni 2 ga bo'lish.

$$x=\frac{\sqrt{3409}}{14}+\frac{1}{2}$$

x=\frac{1±\frac{\sqrt{3409}}{7}}{2} tenglamasini yeching, bunda ± manfiy. 1 dan \frac{\sqrt{3409}}{7} ni ayirish.

$$x=\frac{-\frac{\sqrt{3409}}{7}+1}{2}$$

1-\frac{\sqrt{3409}}{7} ni 2 ga bo'lish.

$$x=-\frac{\sqrt{3409}}{14}+\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{3409}}{14}+\frac{1}{2} x=-\frac{\sqrt{3409}}{14}+\frac{1}{2}$$

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.

$$x^{2}-x=\frac{120}{7}$$

-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.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{120}{7}+\left(-\frac{1}{2}\right)^{2}$$

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

$$x^{2}-x+\frac{1}{4}=\frac{120}{7}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{120}{7} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-x+\frac{1}{4}=\frac{487}{28}$$

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.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{487}{28}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{487}{28}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{3409}}{14} x-\frac{1}{2}=-\frac{\sqrt{3409}}{14}$$

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

$$x=\frac{\sqrt{3409}}{14}+\frac{1}{2} x=-\frac{\sqrt{3409}}{14}+\frac{1}{2}$$