7*x^2-5*x+6=0 eching

$$7 \times { x }^{ 2 } -5 \times x+6=0$$

x uchun yechish (complex solution)

$$x=\frac{5+\sqrt{143}i}{14}\approx 0,357142857+0,854161482i$$

$$x=\frac{-\sqrt{143}i+5}{14}\approx 0,357142857-0,854161482i$$

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.

$$7x^{2}-5x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -5 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 7\times 6}}{2\times 7}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 7\times 6}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-28\times 6}}{2\times 7}$$

-28 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-168}}{2\times 7}$$

25 ni -168 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{-143}}{2\times 7}$$

-143 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{143}i}{2\times 7}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±\sqrt{143}i}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{5±\sqrt{143}i}{14}$$

x=\frac{5±\sqrt{143}i}{14} tenglamasini yeching, bunda ± musbat. 5 ni i\sqrt{143} ga qo'shish.

$$x=\frac{5+\sqrt{143}i}{14}$$

x=\frac{5±\sqrt{143}i}{14} tenglamasini yeching, bunda ± manfiy. 5 dan i\sqrt{143} ni ayirish.

$$x=\frac{-\sqrt{143}i+5}{14}$$

Tenglama yechildi.

$$x=\frac{5+\sqrt{143}i}{14} x=\frac{-\sqrt{143}i+5}{14}$$

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.

$$7x^{2}-5x+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$7x^{2}-5x+6-6=-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$7x^{2}-5x=-6$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-5x}{7}=-\frac{6}{7}$$

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

$$x^{2}-\frac{5}{7}x=-\frac{6}{7}$$

-\frac{5}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{14} olish uchun. Keyin, -\frac{5}{14} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{7}x+\left(-\frac{5}{14}\right)^{2}=-\frac{6}{7}+\left(-\frac{5}{14}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{14} kvadratini chiqarish.

$$x^{2}-\frac{5}{7}x+\frac{25}{196}=-\frac{6}{7}+\frac{25}{196}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{6}{7} ni \frac{25}{196} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{5}{7}x+\frac{25}{196}=-\frac{143}{196}$$

x^{2}-\frac{5}{7}x+\frac{25}{196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{5}{14}\right)^{2}=-\frac{143}{196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{14}\right)^{2}}=\sqrt{-\frac{143}{196}}$$

Qisqartirish.

$$x-\frac{5}{14}=\frac{\sqrt{143}i}{14} x-\frac{5}{14}=-\frac{\sqrt{143}i}{14}$$

\frac{5}{14} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5+\sqrt{143}i}{14} x=\frac{-\sqrt{143}i+5}{14}$$