6794+x^2=165x eching

$$6794+ { x }^{ 2 } =165x$$

x uchun yechish

$$x=79$$

$$x=86$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 165x ni ayirish.

$$6794+x^{2}-165x=0$$

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.

$$x^{2}-165x+6794=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -165 ni b va 6794 ni c bilan almashtiring.

$$x=\frac{-\left(-165\right)±\sqrt{\left(-165\right)^{2}-4\times 6794}}{2}$$

-165 kvadratini chiqarish.

$$x=\frac{-\left(-165\right)±\sqrt{27225-4\times 6794}}{2}$$

-4 ni 6794 marotabaga ko'paytirish.

$$x=\frac{-\left(-165\right)±\sqrt{27225-27176}}{2}$$

27225 ni -27176 ga qo'shish.

$$x=\frac{-\left(-165\right)±\sqrt{49}}{2}$$

49 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-165\right)±7}{2}$$

-165 ning teskarisi 165 ga teng.

$$x=\frac{165±7}{2}$$

x=\frac{165±7}{2} tenglamasini yeching, bunda ± musbat. 165 ni 7 ga qo'shish.

$$x=\frac{172}{2}$$

172 ni 2 ga bo'lish.

$$x=86$$

x=\frac{165±7}{2} tenglamasini yeching, bunda ± manfiy. 165 dan 7 ni ayirish.

$$x=\frac{158}{2}$$

158 ni 2 ga bo'lish.

$$x=79$$

Tenglama yechildi.

$$x=86 x=79$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 165x ni ayirish.

$$6794+x^{2}-165x=0$$

Ikkala tarafdan 6794 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-165x=-6794$$

-165 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{165}{2} olish uchun. Keyin, -\frac{165}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-165x+\left(-\frac{165}{2}\right)^{2}=-6794+\left(-\frac{165}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{165}{2} kvadratini chiqarish.

$$x^{2}-165x+\frac{27225}{4}=-6794+\frac{27225}{4}$$

-6794 ni \frac{27225}{4} ga qo'shish.

$$x^{2}-165x+\frac{27225}{4}=\frac{49}{4}$$

x^{2}-165x+\frac{27225}{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.

$$\left(x-\frac{165}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{165}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{165}{2}=\frac{7}{2} x-\frac{165}{2}=-\frac{7}{2}$$

\frac{165}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=86 x=79$$