(x-8)^2=x eching

$$( x - 8 ) ^ { 2 } = x$$

x uchun yechish

$$x = \frac{\sqrt{33} + 17}{2} \approx 11,372281323$$

$$x = \frac{17 - \sqrt{33}}{2} \approx 5,627718677$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-8\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-16x+64=x$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-16x+64-x=0$$

-17x ni olish uchun -16x va -x ni birlashtirish.

$$x^{2}-17x+64=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -17 ni b va 64 ni c bilan almashtiring.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 64}}{2}$$

-17 kvadratini chiqarish.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\times 64}}{2}$$

-4 ni 64 marotabaga ko'paytirish.

$$x=\frac{-\left(-17\right)±\sqrt{289-256}}{2}$$

289 ni -256 ga qo'shish.

$$x=\frac{-\left(-17\right)±\sqrt{33}}{2}$$

-17 ning teskarisi 17 ga teng.

$$x=\frac{17±\sqrt{33}}{2}$$

x=\frac{17±\sqrt{33}}{2} tenglamasini yeching, bunda ± musbat. 17 ni \sqrt{33} ga qo'shish.

$$x=\frac{\sqrt{33}+17}{2}$$

x=\frac{17±\sqrt{33}}{2} tenglamasini yeching, bunda ± manfiy. 17 dan \sqrt{33} ni ayirish.

$$x=\frac{17-\sqrt{33}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{33}+17}{2} x=\frac{17-\sqrt{33}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-8\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-16x+64=x$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-16x+64-x=0$$

-17x ni olish uchun -16x va -x ni birlashtirish.

$$x^{2}-17x+64=0$$

Ikkala tarafdan 64 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-17x=-64$$

-17 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{17}{2} olish uchun. Keyin, -\frac{17}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-17x+\left(-\frac{17}{2}\right)^{2}=-64+\left(-\frac{17}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{17}{2} kvadratini chiqarish.

$$x^{2}-17x+\frac{289}{4}=-64+\frac{289}{4}$$

-64 ni \frac{289}{4} ga qo'shish.

$$x^{2}-17x+\frac{289}{4}=\frac{33}{4}$$

x^{2}-17x+\frac{289}{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.

$$\left(x-\frac{17}{2}\right)^{2}=\frac{33}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{17}{2}\right)^{2}}=\sqrt{\frac{33}{4}}$$

Qisqartirish.

$$x-\frac{17}{2}=\frac{\sqrt{33}}{2} x-\frac{17}{2}=-\frac{\sqrt{33}}{2}$$

\frac{17}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{33}+17}{2} x=\frac{17-\sqrt{33}}{2}$$