125x^2-11x+10=0 eching

$$125 x ^ { 2 } - 11 x + 10 = 0$$

x uchun yechish (complex solution)

$$x=\frac{11+\sqrt{4879}i}{250}\approx 0,044+0,279399356i$$

$$x=\frac{-\sqrt{4879}i+11}{250}\approx 0,044-0,279399356i$$

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.

$$125x^{2}-11x+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 125 ni a, -11 ni b va 10 ni c bilan almashtiring.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 125\times 10}}{2\times 125}$$

-11 kvadratini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 125\times 10}}{2\times 125}$$

-4 ni 125 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121-500\times 10}}{2\times 125}$$

-500 ni 10 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121-5000}}{2\times 125}$$

121 ni -5000 ga qo'shish.

$$x=\frac{-\left(-11\right)±\sqrt{-4879}}{2\times 125}$$

-4879 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{4879}i}{2\times 125}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±\sqrt{4879}i}{2\times 125}$$

2 ni 125 marotabaga ko'paytirish.

$$x=\frac{11±\sqrt{4879}i}{250}$$

x=\frac{11±\sqrt{4879}i}{250} tenglamasini yeching, bunda ± musbat. 11 ni i\sqrt{4879} ga qo'shish.

$$x=\frac{11+\sqrt{4879}i}{250}$$

x=\frac{11±\sqrt{4879}i}{250} tenglamasini yeching, bunda ± manfiy. 11 dan i\sqrt{4879} ni ayirish.

$$x=\frac{-\sqrt{4879}i+11}{250}$$

Tenglama yechildi.

$$x=\frac{11+\sqrt{4879}i}{250} x=\frac{-\sqrt{4879}i+11}{250}$$

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.

$$125x^{2}-11x+10=0$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$125x^{2}-11x+10-10=-10$$

O‘zidan 10 ayirilsa 0 qoladi.

$$125x^{2}-11x=-10$$

Ikki tarafini 125 ga bo‘ling.

$$\frac{125x^{2}-11x}{125}=-\frac{10}{125}$$

125 ga bo'lish 125 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{11}{125}x=-\frac{10}{125}$$

\frac{-10}{125} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{11}{125}x=-\frac{2}{25}$$

-\frac{11}{125} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{11}{250} olish uchun. Keyin, -\frac{11}{250} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{11}{125}x+\left(-\frac{11}{250}\right)^{2}=-\frac{2}{25}+\left(-\frac{11}{250}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{11}{250} kvadratini chiqarish.

$$x^{2}-\frac{11}{125}x+\frac{121}{62500}=-\frac{2}{25}+\frac{121}{62500}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{2}{25} ni \frac{121}{62500} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{11}{125}x+\frac{121}{62500}=-\frac{4879}{62500}$$

x^{2}-\frac{11}{125}x+\frac{121}{62500} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{11}{250}\right)^{2}=-\frac{4879}{62500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{11}{250}\right)^{2}}=\sqrt{-\frac{4879}{62500}}$$

Qisqartirish.

$$x-\frac{11}{250}=\frac{\sqrt{4879}i}{250} x-\frac{11}{250}=-\frac{\sqrt{4879}i}{250}$$

\frac{11}{250} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{11+\sqrt{4879}i}{250} x=\frac{-\sqrt{4879}i+11}{250}$$