3x^2-8=7x eching

$$3 x ^ { 2 } - 8 = 7 x$$

x uchun yechish

$$x = \frac{\sqrt{145} + 7}{6} \approx 3,173599096$$

$$x=\frac{7-\sqrt{145}}{6}\approx -0,840265763$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 7x ni ayirish.

$$3x^{2}-8-7x=0$$

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.

$$3x^{2}-7x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -7 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 3\left(-8\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49-12\left(-8\right)}}{2\times 3}$$

-12 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+96}}{2\times 3}$$

49 ni 96 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{145}}{2\times 3}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{145}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{7±\sqrt{145}}{6}$$

x=\frac{7±\sqrt{145}}{6} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{145} ga qo'shish.

$$x=\frac{\sqrt{145}+7}{6}$$

x=\frac{7±\sqrt{145}}{6} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{145} ni ayirish.

$$x=\frac{7-\sqrt{145}}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{145}+7}{6} x=\frac{7-\sqrt{145}}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 7x ni ayirish.

$$3x^{2}-8-7x=0$$

8 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$3x^{2}-7x=8$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-7x}{3}=\frac{8}{3}$$

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

$$x^{2}-\frac{7}{3}x=\frac{8}{3}$$

-\frac{7}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{6} olish uchun. Keyin, -\frac{7}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7}{3}x+\left(-\frac{7}{6}\right)^{2}=\frac{8}{3}+\left(-\frac{7}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{6} kvadratini chiqarish.

$$x^{2}-\frac{7}{3}x+\frac{49}{36}=\frac{8}{3}+\frac{49}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{8}{3} ni \frac{49}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{7}{3}x+\frac{49}{36}=\frac{145}{36}$$

x^{2}-\frac{7}{3}x+\frac{49}{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.

$$\left(x-\frac{7}{6}\right)^{2}=\frac{145}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{6}\right)^{2}}=\sqrt{\frac{145}{36}}$$

Qisqartirish.

$$x-\frac{7}{6}=\frac{\sqrt{145}}{6} x-\frac{7}{6}=-\frac{\sqrt{145}}{6}$$

\frac{7}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{145}+7}{6} x=\frac{7-\sqrt{145}}{6}$$