x^2+19x+100=9648 eching

$${ x }^{ 2 } +19x+100=9648$$

x uchun yechish

$$x = \frac{\sqrt{38553} - 19}{2} \approx 88,67458938$$

$$x=\frac{-\sqrt{38553}-19}{2}\approx -107,67458938$$

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.

$$x^{2}+19x+100=9648$$

Tenglamaning ikkala tarafidan 9648 ni ayirish.

$$x^{2}+19x+100-9648=9648-9648$$

O‘zidan 9648 ayirilsa 0 qoladi.

$$x^{2}+19x+100-9648=0$$

100 dan 9648 ni ayirish.

$$x^{2}+19x-9548=0$$

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 -9548 ni c bilan almashtiring.

$$x=\frac{-19±\sqrt{19^{2}-4\left(-9548\right)}}{2}$$

19 kvadratini chiqarish.

$$x=\frac{-19±\sqrt{361-4\left(-9548\right)}}{2}$$

-4 ni -9548 marotabaga ko'paytirish.

$$x=\frac{-19±\sqrt{361+38192}}{2}$$

361 ni 38192 ga qo'shish.

$$x=\frac{-19±\sqrt{38553}}{2}$$

x=\frac{-19±\sqrt{38553}}{2} tenglamasini yeching, bunda ± musbat. -19 ni \sqrt{38553} ga qo'shish.

$$x=\frac{\sqrt{38553}-19}{2}$$

x=\frac{-19±\sqrt{38553}}{2} tenglamasini yeching, bunda ± manfiy. -19 dan \sqrt{38553} ni ayirish.

$$x=\frac{-\sqrt{38553}-19}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{38553}-19}{2} x=\frac{-\sqrt{38553}-19}{2}$$

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.

$$x^{2}+19x+100=9648$$

Tenglamaning ikkala tarafidan 100 ni ayirish.

$$x^{2}+19x+100-100=9648-100$$

O‘zidan 100 ayirilsa 0 qoladi.

$$x^{2}+19x=9648-100$$

9648 dan 100 ni ayirish.

$$x^{2}+19x=9548$$

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.

$$x^{2}+19x+\left(\frac{19}{2}\right)^{2}=9548+\left(\frac{19}{2}\right)^{2}$$

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

$$x^{2}+19x+\frac{361}{4}=9548+\frac{361}{4}$$

9548 ni \frac{361}{4} ga qo'shish.

$$x^{2}+19x+\frac{361}{4}=\frac{38553}{4}$$

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.

$$\left(x+\frac{19}{2}\right)^{2}=\frac{38553}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{19}{2}\right)^{2}}=\sqrt{\frac{38553}{4}}$$

Qisqartirish.

$$x+\frac{19}{2}=\frac{\sqrt{38553}}{2} x+\frac{19}{2}=-\frac{\sqrt{38553}}{2}$$

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

$$x=\frac{\sqrt{38553}-19}{2} x=\frac{-\sqrt{38553}-19}{2}$$