1000x(1+x-002)=108 eching

$$1000x(1+x-002)=108$$

x uchun yechish

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2}\approx 0,098331012$$

$$x=-\frac{\sqrt{895}}{50}-\frac{1}{2}\approx -1,098331012$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$1000x\left(1+x-0\times 2\right)=108$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$1000x\left(1+x-0\right)=108$$

Ikkala tarafdan 108 ni ayirish.

$$1000x\left(1+x-0\right)-108=0$$

Shartlarni qayta saralash.

$$1000x\left(x+1\right)-108=0$$

1000x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1000x^{2}+1000x-108=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1000 ni a, 1000 ni b va -108 ni c bilan almashtiring.

$$x=\frac{-1000±\sqrt{1000^{2}-4\times 1000\left(-108\right)}}{2\times 1000}$$

1000 kvadratini chiqarish.

$$x=\frac{-1000±\sqrt{1000000-4\times 1000\left(-108\right)}}{2\times 1000}$$

-4 ni 1000 marotabaga ko'paytirish.

$$x=\frac{-1000±\sqrt{1000000-4000\left(-108\right)}}{2\times 1000}$$

-4000 ni -108 marotabaga ko'paytirish.

$$x=\frac{-1000±\sqrt{1000000+432000}}{2\times 1000}$$

1000000 ni 432000 ga qo'shish.

$$x=\frac{-1000±\sqrt{1432000}}{2\times 1000}$$

1432000 ning kvadrat ildizini chiqarish.

$$x=\frac{-1000±40\sqrt{895}}{2\times 1000}$$

2 ni 1000 marotabaga ko'paytirish.

$$x=\frac{-1000±40\sqrt{895}}{2000}$$

x=\frac{-1000±40\sqrt{895}}{2000} tenglamasini yeching, bunda ± musbat. -1000 ni 40\sqrt{895} ga qo'shish.

$$x=\frac{40\sqrt{895}-1000}{2000}$$

-1000+40\sqrt{895} ni 2000 ga bo'lish.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2}$$

x=\frac{-1000±40\sqrt{895}}{2000} tenglamasini yeching, bunda ± manfiy. -1000 dan 40\sqrt{895} ni ayirish.

$$x=\frac{-40\sqrt{895}-1000}{2000}$$

-1000-40\sqrt{895} ni 2000 ga bo'lish.

$$x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2} x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$1000x\left(1+x-0\times 2\right)=108$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$1000x\left(1+x-0\right)=108$$

Shartlarni qayta saralash.

$$1000x\left(x+1\right)=108$$

1000x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1000x^{2}+1000x=108$$

Ikki tarafini 1000 ga bo‘ling.

$$\frac{1000x^{2}+1000x}{1000}=\frac{108}{1000}$$

1000 ga bo'lish 1000 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1000}{1000}x=\frac{108}{1000}$$

1000 ni 1000 ga bo'lish.

$$x^{2}+x=\frac{108}{1000}$$

\frac{108}{1000} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+x=\frac{27}{250}$$

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{27}{250}+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=\frac{27}{250}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{27}{250} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+x+\frac{1}{4}=\frac{179}{500}$$

x^{2}+x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{179}{500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{179}{500}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{\sqrt{895}}{50} x+\frac{1}{2}=-\frac{\sqrt{895}}{50}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=\frac{\sqrt{895}}{50}-\frac{1}{2} x=-\frac{\sqrt{895}}{50}-\frac{1}{2}$$