9x^2-2=18x eching

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

x uchun yechish

$$x=\frac{\sqrt{11}}{3}+1\approx 2,105541597$$

$$x=-\frac{\sqrt{11}}{3}+1\approx -0,105541597$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 18x ni ayirish.

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

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.

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

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 -2 ni c bilan almashtiring.

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

-18 kvadratini chiqarish.

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

-4 ni 9 marotabaga ko'paytirish.

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

-36 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324+72}}{2\times 9}$$

324 ni 72 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{396}}{2\times 9}$$

396 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±6\sqrt{11}}{2\times 9}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±6\sqrt{11}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{18±6\sqrt{11}}{18}$$

x=\frac{18±6\sqrt{11}}{18} tenglamasini yeching, bunda ± musbat. 18 ni 6\sqrt{11} ga qo'shish.

$$x=\frac{6\sqrt{11}+18}{18}$$

18+6\sqrt{11} ni 18 ga bo'lish.

$$x=\frac{\sqrt{11}}{3}+1$$

x=\frac{18±6\sqrt{11}}{18} tenglamasini yeching, bunda ± manfiy. 18 dan 6\sqrt{11} ni ayirish.

$$x=\frac{18-6\sqrt{11}}{18}$$

18-6\sqrt{11} ni 18 ga bo'lish.

$$x=-\frac{\sqrt{11}}{3}+1$$

Tenglama yechildi.

$$x=\frac{\sqrt{11}}{3}+1 x=-\frac{\sqrt{11}}{3}+1$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 18x ni ayirish.

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

2 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

Ikki tarafini 9 ga bo‘ling.

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

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

$$x^{2}+\left(-\frac{18}{9}\right)x=\frac{2}{9}$$

-18 ni 9 ga bo'lish.

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

-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.

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

\frac{2}{9} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{11}{9}$$

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.

$$\left(x-1\right)^{2}=\frac{11}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{11}{9}}$$

Qisqartirish.

$$x-1=\frac{\sqrt{11}}{3} x-1=-\frac{\sqrt{11}}{3}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{11}}{3}+1 x=-\frac{\sqrt{11}}{3}+1$$