6000(1-x)*(1-x)=4860 eching

$$6000(1-x) \times (1-x)=4860$$

x uchun yechish

$$x=\frac{1}{10}=0,1$$

$$x = \frac{19}{10} = 1\frac{9}{10} = 1,9$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(1-x\right)^{2} hosil qilish uchun 1-x va 1-x ni ko'paytirish.

$$6000\left(1-x\right)^{2}=4860$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(1-x\right)^{2} kengaytirilishi uchun ishlating.

$$6000\left(1-2x+x^{2}\right)=4860$$

6000 ga 1-2x+x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6000-12000x+6000x^{2}=4860$$

Ikkala tarafdan 4860 ni ayirish.

$$6000-12000x+6000x^{2}-4860=0$$

1140 olish uchun 6000 dan 4860 ni ayirish.

$$1140-12000x+6000x^{2}=0$$

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.

$$6000x^{2}-12000x+1140=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6000 ni a, -12000 ni b va 1140 ni c bilan almashtiring.

$$x=\frac{-\left(-12000\right)±\sqrt{\left(-12000\right)^{2}-4\times 6000\times 1140}}{2\times 6000}$$

-12000 kvadratini chiqarish.

$$x=\frac{-\left(-12000\right)±\sqrt{144000000-4\times 6000\times 1140}}{2\times 6000}$$

-4 ni 6000 marotabaga ko'paytirish.

$$x=\frac{-\left(-12000\right)±\sqrt{144000000-24000\times 1140}}{2\times 6000}$$

-24000 ni 1140 marotabaga ko'paytirish.

$$x=\frac{-\left(-12000\right)±\sqrt{144000000-27360000}}{2\times 6000}$$

144000000 ni -27360000 ga qo'shish.

$$x=\frac{-\left(-12000\right)±\sqrt{116640000}}{2\times 6000}$$

116640000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12000\right)±10800}{2\times 6000}$$

-12000 ning teskarisi 12000 ga teng.

$$x=\frac{12000±10800}{2\times 6000}$$

2 ni 6000 marotabaga ko'paytirish.

$$x=\frac{12000±10800}{12000}$$

x=\frac{12000±10800}{12000} tenglamasini yeching, bunda ± musbat. 12000 ni 10800 ga qo'shish.

$$x=\frac{22800}{12000}$$

\frac{22800}{12000} ulushini 1200 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{19}{10}$$

x=\frac{12000±10800}{12000} tenglamasini yeching, bunda ± manfiy. 12000 dan 10800 ni ayirish.

$$x=\frac{1200}{12000}$$

\frac{1200}{12000} ulushini 1200 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{10}$$

Tenglama yechildi.

$$x=\frac{19}{10} x=\frac{1}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(1-x\right)^{2} hosil qilish uchun 1-x va 1-x ni ko'paytirish.

$$6000\left(1-x\right)^{2}=4860$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(1-x\right)^{2} kengaytirilishi uchun ishlating.

$$6000\left(1-2x+x^{2}\right)=4860$$

6000 ga 1-2x+x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6000-12000x+6000x^{2}=4860$$

Ikkala tarafdan 6000 ni ayirish.

$$-12000x+6000x^{2}=4860-6000$$

-1140 olish uchun 4860 dan 6000 ni ayirish.

$$-12000x+6000x^{2}=-1140$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$6000x^{2}-12000x=-1140$$

Ikki tarafini 6000 ga bo‘ling.

$$\frac{6000x^{2}-12000x}{6000}=-\frac{1140}{6000}$$

6000 ga bo'lish 6000 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12000}{6000}\right)x=-\frac{1140}{6000}$$

-12000 ni 6000 ga bo'lish.

$$x^{2}-2x=-\frac{1140}{6000}$$

\frac{-1140}{6000} ulushini 60 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-2x=-\frac{19}{100}$$

-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.

$$x^{2}-2x+1=-\frac{19}{100}+1$$

-\frac{19}{100} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{81}{100}$$

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.

$$\left(x-1\right)^{2}=\frac{81}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{81}{100}}$$

Qisqartirish.

$$x-1=\frac{9}{10} x-1=-\frac{9}{10}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{19}{10} x=\frac{1}{10}$$