0=9left(x+1right)^2-8 eching

$$0=9 { \left(x+1 \right) }^{ 2 } -8$$

x uchun yechish

$$x=\frac{2\sqrt{2}}{3}-1\approx -0,057190958$$

$$x=-\frac{2\sqrt{2}}{3}-1\approx -1,942809042$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$0=9\left(x^{2}+2x+1\right)-8$$

9 ga x^{2}+2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0=9x^{2}+18x+9-8$$

1 olish uchun 9 dan 8 ni ayirish.

$$0=9x^{2}+18x+1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9x^{2}+18x+1=0$$

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 1 ni c bilan almashtiring.

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

18 kvadratini chiqarish.

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

-4 ni 9 marotabaga ko'paytirish.

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

324 ni -36 ga qo'shish.

$$x=\frac{-18±\sqrt{288}}{2\times 9}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±12\sqrt{2}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±12\sqrt{2}}{18}$$

x=\frac{-18±12\sqrt{2}}{18} tenglamasini yeching, bunda ± musbat. -18 ni 12\sqrt{2} ga qo'shish.

$$x=\frac{12\sqrt{2}-18}{18}$$

-18+12\sqrt{2} ni 18 ga bo'lish.

$$x=\frac{2\sqrt{2}}{3}-1$$

x=\frac{-18±12\sqrt{2}}{18} tenglamasini yeching, bunda ± manfiy. -18 dan 12\sqrt{2} ni ayirish.

$$x=\frac{-12\sqrt{2}-18}{18}$$

-18-12\sqrt{2} ni 18 ga bo'lish.

$$x=-\frac{2\sqrt{2}}{3}-1$$

Tenglama yechildi.

$$x=\frac{2\sqrt{2}}{3}-1 x=-\frac{2\sqrt{2}}{3}-1$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$0=9\left(x^{2}+2x+1\right)-8$$

9 ga x^{2}+2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0=9x^{2}+18x+9-8$$

1 olish uchun 9 dan 8 ni ayirish.

$$0=9x^{2}+18x+1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9x^{2}+18x+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$9x^{2}+18x=-1$$

Ikki tarafini 9 ga bo‘ling.

$$\frac{9x^{2}+18x}{9}=-\frac{1}{9}$$

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

$$x^{2}+\frac{18}{9}x=-\frac{1}{9}$$

18 ni 9 ga bo'lish.

$$x^{2}+2x=-\frac{1}{9}$$

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.

$$x^{2}+2x+1^{2}=-\frac{1}{9}+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-\frac{1}{9}+1$$

-\frac{1}{9} ni 1 ga qo'shish.

$$x^{2}+2x+1=\frac{8}{9}$$

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.

$$\left(x+1\right)^{2}=\frac{8}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{\frac{8}{9}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\frac{2\sqrt{2}}{3}-1 x=-\frac{2\sqrt{2}}{3}-1$$