-9x^2+18x-3=0 eching

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

x uchun yechish

$$x=\frac{\sqrt{6}}{3}+1\approx 1,816496581$$

$$x=-\frac{\sqrt{6}}{3}+1\approx 0,183503419$$

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.

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

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 -3 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-9\right)\left(-3\right)}}{2\left(-9\right)}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-9\right)\left(-3\right)}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+36\left(-3\right)}}{2\left(-9\right)}$$

36 ni -3 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-108}}{2\left(-9\right)}$$

324 ni -108 ga qo'shish.

$$x=\frac{-18±\sqrt{216}}{2\left(-9\right)}$$

216 ning kvadrat ildizini chiqarish.

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

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{-18±6\sqrt{6}}{-18}$$

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

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

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

$$x=-\frac{\sqrt{6}}{3}+1$$

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

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

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

$$x=\frac{\sqrt{6}}{3}+1$$

Tenglama yechildi.

$$x=-\frac{\sqrt{6}}{3}+1 x=\frac{\sqrt{6}}{3}+1$$

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.

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

3 ni tenglamaning ikkala tarafiga qo'shish.

$$-9x^{2}+18x-3-\left(-3\right)=-\left(-3\right)$$

O‘zidan -3 ayirilsa 0 qoladi.

$$-9x^{2}+18x=-\left(-3\right)$$

0 dan -3 ni ayirish.

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

Ikki tarafini -9 ga bo‘ling.

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

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

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

18 ni -9 ga bo'lish.

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

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

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

-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.

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

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

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-1=\frac{\sqrt{6}}{3} x-1=-\frac{\sqrt{6}}{3}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{6}}{3}+1 x=-\frac{\sqrt{6}}{3}+1$$