x^2-34=16x eching

$${ x }^{ 2 } -34=16x$$

x uchun yechish

$$x=7\sqrt{2}+8\approx 17,899494937$$

$$x=8-7\sqrt{2}\approx -1,899494937$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 16x ni ayirish.

$$x^{2}-34-16x=0$$

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.

$$x^{2}-16x-34=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -16 ni b va -34 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-34\right)}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-34\right)}}{2}$$

-4 ni -34 marotabaga ko'paytirish.

$$x=\frac{-\left(-16\right)±\sqrt{256+136}}{2}$$

256 ni 136 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{392}}{2}$$

392 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±14\sqrt{2}}{2}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±14\sqrt{2}}{2}$$

x=\frac{16±14\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 16 ni 14\sqrt{2} ga qo'shish.

$$x=\frac{14\sqrt{2}+16}{2}$$

16+14\sqrt{2} ni 2 ga bo'lish.

$$x=7\sqrt{2}+8$$

x=\frac{16±14\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 14\sqrt{2} ni ayirish.

$$x=\frac{16-14\sqrt{2}}{2}$$

16-14\sqrt{2} ni 2 ga bo'lish.

$$x=8-7\sqrt{2}$$

Tenglama yechildi.

$$x=7\sqrt{2}+8 x=8-7\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 16x ni ayirish.

$$x^{2}-34-16x=0$$

34 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}-16x=34$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-16x+\left(-8\right)^{2}=34+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=34+64$$

34 ni 64 ga qo'shish.

$$x^{2}-16x+64=98$$

x^{2}-16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-8\right)^{2}=98$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{98}$$

Qisqartirish.

$$x-8=7\sqrt{2} x-8=-7\sqrt{2}$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=7\sqrt{2}+8 x=8-7\sqrt{2}$$