x^2-16x+50=21 eching

$$x ^ { 2 } - 16 x + 50 = 21$$

x uchun yechish

$$x=\sqrt{35}+8\approx 13,916079783$$

$$x=8-\sqrt{35}\approx 2,083920217$$

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.

$$x^{2}-16x+50=21$$

Tenglamaning ikkala tarafidan 21 ni ayirish.

$$x^{2}-16x+50-21=21-21$$

O‘zidan 21 ayirilsa 0 qoladi.

$$x^{2}-16x+50-21=0$$

50 dan 21 ni ayirish.

$$x^{2}-16x+29=0$$

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 29 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 29}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\times 29}}{2}$$

-4 ni 29 marotabaga ko'paytirish.

$$x=\frac{-\left(-16\right)±\sqrt{256-116}}{2}$$

256 ni -116 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{140}}{2}$$

140 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±2\sqrt{35}}{2}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±2\sqrt{35}}{2}$$

x=\frac{16±2\sqrt{35}}{2} tenglamasini yeching, bunda ± musbat. 16 ni 2\sqrt{35} ga qo'shish.

$$x=\frac{2\sqrt{35}+16}{2}$$

16+2\sqrt{35} ni 2 ga bo'lish.

$$x=\sqrt{35}+8$$

x=\frac{16±2\sqrt{35}}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 2\sqrt{35} ni ayirish.

$$x=\frac{16-2\sqrt{35}}{2}$$

16-2\sqrt{35} ni 2 ga bo'lish.

$$x=8-\sqrt{35}$$

Tenglama yechildi.

$$x=\sqrt{35}+8 x=8-\sqrt{35}$$

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.

$$x^{2}-16x+50=21$$

Tenglamaning ikkala tarafidan 50 ni ayirish.

$$x^{2}-16x+50-50=21-50$$

O‘zidan 50 ayirilsa 0 qoladi.

$$x^{2}-16x=21-50$$

21 dan 50 ni ayirish.

$$x^{2}-16x=-29$$

-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.

$$x^{2}-16x+\left(-8\right)^{2}=-29+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=-29+64$$

-29 ni 64 ga qo'shish.

$$x^{2}-16x+64=35$$

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.

$$\left(x-8\right)^{2}=35$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{35}$$

Qisqartirish.

$$x-8=\sqrt{35} x-8=-\sqrt{35}$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{35}+8 x=8-\sqrt{35}$$