(x-1)^2=16x eching

$$( x - 1 ) ^ { 2 } = 16 x$$

x uchun yechish

$$x=4\sqrt{5}+9\approx 17,94427191$$

$$x=9-4\sqrt{5}\approx 0,05572809$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-2x+1=16x$$

Ikkala tarafdan 16x ni ayirish.

$$x^{2}-2x+1-16x=0$$

-18x ni olish uchun -2x va -16x ni birlashtirish.

$$x^{2}-18x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -18 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4}}{2}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4}}{2}$$

324 ni -4 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{320}}{2}$$

320 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±8\sqrt{5}}{2}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±8\sqrt{5}}{2}$$

x=\frac{18±8\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. 18 ni 8\sqrt{5} ga qo'shish.

$$x=\frac{8\sqrt{5}+18}{2}$$

18+8\sqrt{5} ni 2 ga bo'lish.

$$x=4\sqrt{5}+9$$

x=\frac{18±8\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 8\sqrt{5} ni ayirish.

$$x=\frac{18-8\sqrt{5}}{2}$$

18-8\sqrt{5} ni 2 ga bo'lish.

$$x=9-4\sqrt{5}$$

Tenglama yechildi.

$$x=4\sqrt{5}+9 x=9-4\sqrt{5}$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-2x+1=16x$$

Ikkala tarafdan 16x ni ayirish.

$$x^{2}-2x+1-16x=0$$

-18x ni olish uchun -2x va -16x ni birlashtirish.

$$x^{2}-18x+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-18x=-1$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-18x+\left(-9\right)^{2}=-1+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=-1+81$$

-1 ni 81 ga qo'shish.

$$x^{2}-18x+81=80$$

x^{2}-18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-9\right)^{2}=80$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{80}$$

Qisqartirish.

$$x-9=4\sqrt{5} x-9=-4\sqrt{5}$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{5}+9 x=9-4\sqrt{5}$$