xleft(x+1right)/2=1923(x-1) eching

$$\frac{ x \left( x+1 \right) }{ 2 } = 1923(x-1)$$

x uchun yechish

$$x = \frac{\sqrt{14768641} + 3845}{2} \approx 3843,999479573$$

$$x = \frac{3845 - \sqrt{14768641}}{2} \approx 1,000520427$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$x\left(x+1\right)=3846\left(x-1\right)$$

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

$$x^{2}+x=3846\left(x-1\right)$$

3846 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x=3846x-3846$$

Ikkala tarafdan 3846x ni ayirish.

$$x^{2}+x-3846x=-3846$$

-3845x ni olish uchun x va -3846x ni birlashtirish.

$$x^{2}-3845x=-3846$$

3846 ni ikki tarafga qo’shing.

$$x^{2}-3845x+3846=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3845 ni b va 3846 ni c bilan almashtiring.

$$x=\frac{-\left(-3845\right)±\sqrt{\left(-3845\right)^{2}-4\times 3846}}{2}$$

-3845 kvadratini chiqarish.

$$x=\frac{-\left(-3845\right)±\sqrt{14784025-4\times 3846}}{2}$$

-4 ni 3846 marotabaga ko'paytirish.

$$x=\frac{-\left(-3845\right)±\sqrt{14784025-15384}}{2}$$

14784025 ni -15384 ga qo'shish.

$$x=\frac{-\left(-3845\right)±\sqrt{14768641}}{2}$$

-3845 ning teskarisi 3845 ga teng.

$$x=\frac{3845±\sqrt{14768641}}{2}$$

x=\frac{3845±\sqrt{14768641}}{2} tenglamasini yeching, bunda ± musbat. 3845 ni \sqrt{14768641} ga qo'shish.

$$x=\frac{\sqrt{14768641}+3845}{2}$$

x=\frac{3845±\sqrt{14768641}}{2} tenglamasini yeching, bunda ± manfiy. 3845 dan \sqrt{14768641} ni ayirish.

$$x=\frac{3845-\sqrt{14768641}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{14768641}+3845}{2} x=\frac{3845-\sqrt{14768641}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$x\left(x+1\right)=3846\left(x-1\right)$$

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

$$x^{2}+x=3846\left(x-1\right)$$

3846 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x=3846x-3846$$

Ikkala tarafdan 3846x ni ayirish.

$$x^{2}+x-3846x=-3846$$

-3845x ni olish uchun x va -3846x ni birlashtirish.

$$x^{2}-3845x=-3846$$

-3845 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3845}{2} olish uchun. Keyin, -\frac{3845}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3845x+\left(-\frac{3845}{2}\right)^{2}=-3846+\left(-\frac{3845}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3845}{2} kvadratini chiqarish.

$$x^{2}-3845x+\frac{14784025}{4}=-3846+\frac{14784025}{4}$$

-3846 ni \frac{14784025}{4} ga qo'shish.

$$x^{2}-3845x+\frac{14784025}{4}=\frac{14768641}{4}$$

x^{2}-3845x+\frac{14784025}{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.

$$\left(x-\frac{3845}{2}\right)^{2}=\frac{14768641}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3845}{2}\right)^{2}}=\sqrt{\frac{14768641}{4}}$$

Qisqartirish.

$$x-\frac{3845}{2}=\frac{\sqrt{14768641}}{2} x-\frac{3845}{2}=-\frac{\sqrt{14768641}}{2}$$

\frac{3845}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{14768641}+3845}{2} x=\frac{3845-\sqrt{14768641}}{2}$$