3x^2-18x+225=6 eching

$$3 x ^ { 2 } - 18 x + 225 = 6$$

x uchun yechish (complex solution)

$$x=3+8i$$

$$x=3-8i$$

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.

$$3x^{2}-18x+225=6$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$3x^{2}-18x+225-6=6-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$3x^{2}-18x+225-6=0$$

225 dan 6 ni ayirish.

$$3x^{2}-18x+219=0$$

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 219 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 3\times 219}}{2\times 3}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 3\times 219}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-12\times 219}}{2\times 3}$$

-12 ni 219 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-2628}}{2\times 3}$$

324 ni -2628 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{-2304}}{2\times 3}$$

-2304 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±48i}{2\times 3}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±48i}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{18±48i}{6}$$

x=\frac{18±48i}{6} tenglamasini yeching, bunda ± musbat. 18 ni 48i ga qo'shish.

$$x=\frac{18+48i}{6}$$

18+48i ni 6 ga bo'lish.

$$x=3+8i$$

x=\frac{18±48i}{6} tenglamasini yeching, bunda ± manfiy. 18 dan 48i ni ayirish.

$$x=\frac{18-48i}{6}$$

18-48i ni 6 ga bo'lish.

$$x=3-8i$$

Tenglama yechildi.

$$x=3+8i x=3-8i$$

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.

$$3x^{2}-18x+225=6$$

Tenglamaning ikkala tarafidan 225 ni ayirish.

$$3x^{2}-18x+225-225=6-225$$

O‘zidan 225 ayirilsa 0 qoladi.

$$3x^{2}-18x=6-225$$

6 dan 225 ni ayirish.

$$3x^{2}-18x=-219$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-18x}{3}=-\frac{219}{3}$$

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

$$x^{2}+\left(-\frac{18}{3}\right)x=-\frac{219}{3}$$

-18 ni 3 ga bo'lish.

$$x^{2}-6x=-\frac{219}{3}$$

-219 ni 3 ga bo'lish.

$$x^{2}-6x=-73$$

-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.

$$x^{2}-6x+\left(-3\right)^{2}=-73+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-73+9$$

-73 ni 9 ga qo'shish.

$$x^{2}-6x+9=-64$$

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.

$$\left(x-3\right)^{2}=-64$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{-64}$$

Qisqartirish.

$$x-3=8i x-3=-8i$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=3+8i x=3-8i$$