3x^2-36x+95=0 eching

$$3 x ^ { 2 } - 36 x + 95 = 0$$

x uchun yechish

$$x=\frac{\sqrt{39}}{3}+6\approx 8,081665999$$

$$x=-\frac{\sqrt{39}}{3}+6\approx 3,918334001$$

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.

$$3x^{2}-36x+95=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -36 ni b va 95 ni c bilan almashtiring.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 3\times 95}}{2\times 3}$$

-36 kvadratini chiqarish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 3\times 95}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-12\times 95}}{2\times 3}$$

-12 ni 95 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-1140}}{2\times 3}$$

1296 ni -1140 ga qo'shish.

$$x=\frac{-\left(-36\right)±\sqrt{156}}{2\times 3}$$

156 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-36\right)±2\sqrt{39}}{2\times 3}$$

-36 ning teskarisi 36 ga teng.

$$x=\frac{36±2\sqrt{39}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{36±2\sqrt{39}}{6}$$

x=\frac{36±2\sqrt{39}}{6} tenglamasini yeching, bunda ± musbat. 36 ni 2\sqrt{39} ga qo'shish.

$$x=\frac{2\sqrt{39}+36}{6}$$

36+2\sqrt{39} ni 6 ga bo'lish.

$$x=\frac{\sqrt{39}}{3}+6$$

x=\frac{36±2\sqrt{39}}{6} tenglamasini yeching, bunda ± manfiy. 36 dan 2\sqrt{39} ni ayirish.

$$x=\frac{36-2\sqrt{39}}{6}$$

36-2\sqrt{39} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{39}}{3}+6$$

Tenglama yechildi.

$$x=\frac{\sqrt{39}}{3}+6 x=-\frac{\sqrt{39}}{3}+6$$

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.

$$3x^{2}-36x+95=0$$

Tenglamaning ikkala tarafidan 95 ni ayirish.

$$3x^{2}-36x+95-95=-95$$

O‘zidan 95 ayirilsa 0 qoladi.

$$3x^{2}-36x=-95$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-36x}{3}=-\frac{95}{3}$$

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

$$x^{2}+\left(-\frac{36}{3}\right)x=-\frac{95}{3}$$

-36 ni 3 ga bo'lish.

$$x^{2}-12x=-\frac{95}{3}$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=-\frac{95}{3}+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=-\frac{95}{3}+36$$

-\frac{95}{3} ni 36 ga qo'shish.

$$x^{2}-12x+36=\frac{13}{3}$$

x^{2}-12x+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.

$$\left(x-6\right)^{2}=\frac{13}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{\frac{13}{3}}$$

Qisqartirish.

$$x-6=\frac{\sqrt{39}}{3} x-6=-\frac{\sqrt{39}}{3}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{39}}{3}+6 x=-\frac{\sqrt{39}}{3}+6$$