3x^2-18x+2=0 eching

$$3 x ^ { 2 } - 18 x + 2 = 0$$

x uchun yechish

$$x=\frac{5\sqrt{3}}{3}+3\approx 5,886751346$$

$$x=-\frac{5\sqrt{3}}{3}+3\approx 0,113248654$$

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.

$$3x^{2}-18x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -18 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 3\times 2}}{2\times 3}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 3\times 2}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-12\times 2}}{2\times 3}$$

-12 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-24}}{2\times 3}$$

324 ni -24 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{300}}{2\times 3}$$

300 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±10\sqrt{3}}{2\times 3}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±10\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{18±10\sqrt{3}}{6}$$

x=\frac{18±10\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat. 18 ni 10\sqrt{3} ga qo'shish.

$$x=\frac{10\sqrt{3}+18}{6}$$

18+10\sqrt{3} ni 6 ga bo'lish.

$$x=\frac{5\sqrt{3}}{3}+3$$

x=\frac{18±10\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy. 18 dan 10\sqrt{3} ni ayirish.

$$x=\frac{18-10\sqrt{3}}{6}$$

18-10\sqrt{3} ni 6 ga bo'lish.

$$x=-\frac{5\sqrt{3}}{3}+3$$

Tenglama yechildi.

$$x=\frac{5\sqrt{3}}{3}+3 x=-\frac{5\sqrt{3}}{3}+3$$

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.

$$3x^{2}-18x+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$3x^{2}-18x+2-2=-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$3x^{2}-18x=-2$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-18x}{3}=-\frac{2}{3}$$

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

$$x^{2}+\left(-\frac{18}{3}\right)x=-\frac{2}{3}$$

-18 ni 3 ga bo'lish.

$$x^{2}-6x=-\frac{2}{3}$$

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

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

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-\frac{2}{3}+9$$

-\frac{2}{3} ni 9 ga qo'shish.

$$x^{2}-6x+9=\frac{25}{3}$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=\frac{25}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{\frac{25}{3}}$$

Qisqartirish.

$$x-3=\frac{5\sqrt{3}}{3} x-3=-\frac{5\sqrt{3}}{3}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{3}}{3}+3 x=-\frac{5\sqrt{3}}{3}+3$$