9x^2+18x+9=3 eching

$$9 x ^ { 2 } + 18 x + 9 = 3$$

x uchun yechish

$$x=\frac{\sqrt{3}}{3}-1\approx -0,422649731$$

$$x=-\frac{\sqrt{3}}{3}-1\approx -1,577350269$$

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.

$$9x^{2}+18x+9=3$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$9x^{2}+18x+9-3=3-3$$

O‘zidan 3 ayirilsa 0 qoladi.

$$9x^{2}+18x+9-3=0$$

9 dan 3 ni ayirish.

$$9x^{2}+18x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 18 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\times 9\times 6}}{2\times 9}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\times 9\times 6}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-36\times 6}}{2\times 9}$$

-36 ni 6 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-216}}{2\times 9}$$

324 ni -216 ga qo'shish.

$$x=\frac{-18±\sqrt{108}}{2\times 9}$$

108 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±6\sqrt{3}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±6\sqrt{3}}{18}$$

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

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

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

$$x=\frac{\sqrt{3}}{3}-1$$

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

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

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

$$x=-\frac{\sqrt{3}}{3}-1$$

Tenglama yechildi.

$$x=\frac{\sqrt{3}}{3}-1 x=-\frac{\sqrt{3}}{3}-1$$

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.

$$9x^{2}+18x+9=3$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$9x^{2}+18x+9-9=3-9$$

O‘zidan 9 ayirilsa 0 qoladi.

$$9x^{2}+18x=3-9$$

3 dan 9 ni ayirish.

$$9x^{2}+18x=-6$$

Ikki tarafini 9 ga bo‘ling.

$$\frac{9x^{2}+18x}{9}=-\frac{6}{9}$$

9 ga bo'lish 9 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{18}{9}x=-\frac{6}{9}$$

18 ni 9 ga bo'lish.

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

\frac{-6}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=-\frac{2}{3}+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-\frac{2}{3}+1$$

-\frac{2}{3} ni 1 ga qo'shish.

$$x^{2}+2x+1=\frac{1}{3}$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=\frac{1}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{\frac{1}{3}}$$

Qisqartirish.

$$x+1=\frac{\sqrt{3}}{3} x+1=-\frac{\sqrt{3}}{3}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\frac{\sqrt{3}}{3}-1 x=-\frac{\sqrt{3}}{3}-1$$