100x^2-90x+18=0 eching

$$100 x ^ { 2 } - 90 x + 18 = 0$$

x uchun yechish

$$x=\frac{3}{10}=0,3$$

$$x=\frac{3}{5}=0,6$$

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.

$$100x^{2}-90x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 100 ni a, -90 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-\left(-90\right)±\sqrt{\left(-90\right)^{2}-4\times 100\times 18}}{2\times 100}$$

-90 kvadratini chiqarish.

$$x=\frac{-\left(-90\right)±\sqrt{8100-4\times 100\times 18}}{2\times 100}$$

-4 ni 100 marotabaga ko'paytirish.

$$x=\frac{-\left(-90\right)±\sqrt{8100-400\times 18}}{2\times 100}$$

-400 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-90\right)±\sqrt{8100-7200}}{2\times 100}$$

8100 ni -7200 ga qo'shish.

$$x=\frac{-\left(-90\right)±\sqrt{900}}{2\times 100}$$

900 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-90\right)±30}{2\times 100}$$

-90 ning teskarisi 90 ga teng.

$$x=\frac{90±30}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$x=\frac{90±30}{200}$$

x=\frac{90±30}{200} tenglamasini yeching, bunda ± musbat. 90 ni 30 ga qo'shish.

$$x=\frac{120}{200}$$

\frac{120}{200} ulushini 40 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{5}$$

x=\frac{90±30}{200} tenglamasini yeching, bunda ± manfiy. 90 dan 30 ni ayirish.

$$x=\frac{60}{200}$$

\frac{60}{200} ulushini 20 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{10}$$

Tenglama yechildi.

$$x=\frac{3}{5} x=\frac{3}{10}$$

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.

$$100x^{2}-90x+18=0$$

Tenglamaning ikkala tarafidan 18 ni ayirish.

$$100x^{2}-90x+18-18=-18$$

O‘zidan 18 ayirilsa 0 qoladi.

$$100x^{2}-90x=-18$$

Ikki tarafini 100 ga bo‘ling.

$$\frac{100x^{2}-90x}{100}=-\frac{18}{100}$$

100 ga bo'lish 100 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{90}{100}\right)x=-\frac{18}{100}$$

\frac{-90}{100} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{9}{10}x=-\frac{18}{100}$$

\frac{-18}{100} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{9}{10}x=-\frac{9}{50}$$

-\frac{9}{10} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{20} olish uchun. Keyin, -\frac{9}{20} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{9}{10}x+\left(-\frac{9}{20}\right)^{2}=-\frac{9}{50}+\left(-\frac{9}{20}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{20} kvadratini chiqarish.

$$x^{2}-\frac{9}{10}x+\frac{81}{400}=-\frac{9}{50}+\frac{81}{400}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{50} ni \frac{81}{400} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{9}{10}x+\frac{81}{400}=\frac{9}{400}$$

x^{2}-\frac{9}{10}x+\frac{81}{400} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{9}{20}\right)^{2}=\frac{9}{400}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{20}\right)^{2}}=\sqrt{\frac{9}{400}}$$

Qisqartirish.

$$x-\frac{9}{20}=\frac{3}{20} x-\frac{9}{20}=-\frac{3}{20}$$

\frac{9}{20} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3}{5} x=\frac{3}{10}$$