(x+19)x=8100 eching

$$(x+19)x=8100$$

x uchun yechish

$$x=-100$$

$$x=81$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+19 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+19x=8100$$

Ikkala tarafdan 8100 ni ayirish.

$$x^{2}+19x-8100=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 19 ni b va -8100 ni c bilan almashtiring.

$$x=\frac{-19±\sqrt{19^{2}-4\left(-8100\right)}}{2}$$

19 kvadratini chiqarish.

$$x=\frac{-19±\sqrt{361-4\left(-8100\right)}}{2}$$

-4 ni -8100 marotabaga ko'paytirish.

$$x=\frac{-19±\sqrt{361+32400}}{2}$$

361 ni 32400 ga qo'shish.

$$x=\frac{-19±\sqrt{32761}}{2}$$

32761 ning kvadrat ildizini chiqarish.

$$x=\frac{-19±181}{2}$$

x=\frac{-19±181}{2} tenglamasini yeching, bunda ± musbat. -19 ni 181 ga qo'shish.

$$x=\frac{162}{2}$$

162 ni 2 ga bo'lish.

$$x=81$$

x=\frac{-19±181}{2} tenglamasini yeching, bunda ± manfiy. -19 dan 181 ni ayirish.

$$x=-\frac{200}{2}$$

-200 ni 2 ga bo'lish.

$$x=-100$$

Tenglama yechildi.

$$x=81 x=-100$$

Kvadratni yakunlash bo'yicha qadamlar

x+19 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+19x=8100$$

19 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{19}{2} olish uchun. Keyin, \frac{19}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+19x+\left(\frac{19}{2}\right)^{2}=8100+\left(\frac{19}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{19}{2} kvadratini chiqarish.

$$x^{2}+19x+\frac{361}{4}=8100+\frac{361}{4}$$

8100 ni \frac{361}{4} ga qo'shish.

$$x^{2}+19x+\frac{361}{4}=\frac{32761}{4}$$

x^{2}+19x+\frac{361}{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.

$$\left(x+\frac{19}{2}\right)^{2}=\frac{32761}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{19}{2}\right)^{2}}=\sqrt{\frac{32761}{4}}$$

Qisqartirish.

$$x+\frac{19}{2}=\frac{181}{2} x+\frac{19}{2}=-\frac{181}{2}$$

Tenglamaning ikkala tarafidan \frac{19}{2} ni ayirish.

$$x=81 x=-100$$