100x^2-50x+18=0 eching

$$100 x ^ { 2 } - 50 x + 18 = 0$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{47}i}{20}+\frac{1}{4}\approx 0,25+0,34278273i$$

$$x=-\frac{\sqrt{47}i}{20}+\frac{1}{4}\approx 0,25-0,34278273i$$

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.

$$100x^{2}-50x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 100 ni a, -50 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 100\times 18}}{2\times 100}$$

-50 kvadratini chiqarish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 100\times 18}}{2\times 100}$$

-4 ni 100 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-400\times 18}}{2\times 100}$$

-400 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-50\right)±\sqrt{2500-7200}}{2\times 100}$$

2500 ni -7200 ga qo'shish.

$$x=\frac{-\left(-50\right)±\sqrt{-4700}}{2\times 100}$$

-4700 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±10\sqrt{47}i}{2\times 100}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±10\sqrt{47}i}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$x=\frac{50±10\sqrt{47}i}{200}$$

x=\frac{50±10\sqrt{47}i}{200} tenglamasini yeching, bunda ± musbat. 50 ni 10i\sqrt{47} ga qo'shish.

$$x=\frac{50+10\sqrt{47}i}{200}$$

50+10i\sqrt{47} ni 200 ga bo'lish.

$$x=\frac{\sqrt{47}i}{20}+\frac{1}{4}$$

x=\frac{50±10\sqrt{47}i}{200} tenglamasini yeching, bunda ± manfiy. 50 dan 10i\sqrt{47} ni ayirish.

$$x=\frac{-10\sqrt{47}i+50}{200}$$

50-10i\sqrt{47} ni 200 ga bo'lish.

$$x=-\frac{\sqrt{47}i}{20}+\frac{1}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{47}i}{20}+\frac{1}{4} x=-\frac{\sqrt{47}i}{20}+\frac{1}{4}$$

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.

$$100x^{2}-50x+18=0$$

Tenglamaning ikkala tarafidan 18 ni ayirish.

$$100x^{2}-50x+18-18=-18$$

O‘zidan 18 ayirilsa 0 qoladi.

$$100x^{2}-50x=-18$$

Ikki tarafini 100 ga bo‘ling.

$$\frac{100x^{2}-50x}{100}=-\frac{18}{100}$$

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

$$x^{2}+\left(-\frac{50}{100}\right)x=-\frac{18}{100}$$

\frac{-50}{100} ulushini 50 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{2}x=-\frac{18}{100}$$

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

$$x^{2}-\frac{1}{2}x=-\frac{9}{50}$$

-\frac{1}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4} olish uchun. Keyin, -\frac{1}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=-\frac{9}{50}+\left(-\frac{1}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4} kvadratini chiqarish.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=-\frac{9}{50}+\frac{1}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{50} ni \frac{1}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=-\frac{47}{400}$$

x^{2}-\frac{1}{2}x+\frac{1}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4}\right)^{2}=-\frac{47}{400}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{-\frac{47}{400}}$$

Qisqartirish.

$$x-\frac{1}{4}=\frac{\sqrt{47}i}{20} x-\frac{1}{4}=-\frac{\sqrt{47}i}{20}$$

\frac{1}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{47}i}{20}+\frac{1}{4} x=-\frac{\sqrt{47}i}{20}+\frac{1}{4}$$