7x^2-300x+800=0 eching

$$7 x ^ { 2 } - 300 x + 800 = 0$$

x uchun yechish

$$x = \frac{20}{7} = 2\frac{6}{7} \approx 2,857142857$$

$$x=40$$

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.

$$7x^{2}-300x+800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -300 ni b va 800 ni c bilan almashtiring.

$$x=\frac{-\left(-300\right)±\sqrt{\left(-300\right)^{2}-4\times 7\times 800}}{2\times 7}$$

-300 kvadratini chiqarish.

$$x=\frac{-\left(-300\right)±\sqrt{90000-4\times 7\times 800}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-300\right)±\sqrt{90000-28\times 800}}{2\times 7}$$

-28 ni 800 marotabaga ko'paytirish.

$$x=\frac{-\left(-300\right)±\sqrt{90000-22400}}{2\times 7}$$

90000 ni -22400 ga qo'shish.

$$x=\frac{-\left(-300\right)±\sqrt{67600}}{2\times 7}$$

67600 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-300\right)±260}{2\times 7}$$

-300 ning teskarisi 300 ga teng.

$$x=\frac{300±260}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{300±260}{14}$$

x=\frac{300±260}{14} tenglamasini yeching, bunda ± musbat. 300 ni 260 ga qo'shish.

$$x=\frac{560}{14}$$

560 ni 14 ga bo'lish.

$$x=40$$

x=\frac{300±260}{14} tenglamasini yeching, bunda ± manfiy. 300 dan 260 ni ayirish.

$$x=\frac{40}{14}$$

\frac{40}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{20}{7}$$

Tenglama yechildi.

$$x=40 x=\frac{20}{7}$$

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.

$$7x^{2}-300x+800=0$$

Tenglamaning ikkala tarafidan 800 ni ayirish.

$$7x^{2}-300x+800-800=-800$$

O‘zidan 800 ayirilsa 0 qoladi.

$$7x^{2}-300x=-800$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-300x}{7}=-\frac{800}{7}$$

7 ga bo'lish 7 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{300}{7}x=-\frac{800}{7}$$

-\frac{300}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{150}{7} olish uchun. Keyin, -\frac{150}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{300}{7}x+\left(-\frac{150}{7}\right)^{2}=-\frac{800}{7}+\left(-\frac{150}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{150}{7} kvadratini chiqarish.

$$x^{2}-\frac{300}{7}x+\frac{22500}{49}=-\frac{800}{7}+\frac{22500}{49}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{800}{7} ni \frac{22500}{49} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{300}{7}x+\frac{22500}{49}=\frac{16900}{49}$$

x^{2}-\frac{300}{7}x+\frac{22500}{49} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{150}{7}\right)^{2}=\frac{16900}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{150}{7}\right)^{2}}=\sqrt{\frac{16900}{49}}$$

Qisqartirish.

$$x-\frac{150}{7}=\frac{130}{7} x-\frac{150}{7}=-\frac{130}{7}$$

\frac{150}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=40 x=\frac{20}{7}$$