x^2-32x+45=0 eching

$${ x }^{ 2 } -32x+45=0$$

x uchun yechish

$$x=\sqrt{211}+16\approx 30,525839046$$

$$x=16-\sqrt{211}\approx 1,474160954$$

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.

$$x^{2}-32x+45=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -32 ni b va 45 ni c bilan almashtiring.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 45}}{2}$$

-32 kvadratini chiqarish.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\times 45}}{2}$$

-4 ni 45 marotabaga ko'paytirish.

$$x=\frac{-\left(-32\right)±\sqrt{1024-180}}{2}$$

1024 ni -180 ga qo'shish.

$$x=\frac{-\left(-32\right)±\sqrt{844}}{2}$$

844 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-32\right)±2\sqrt{211}}{2}$$

-32 ning teskarisi 32 ga teng.

$$x=\frac{32±2\sqrt{211}}{2}$$

x=\frac{32±2\sqrt{211}}{2} tenglamasini yeching, bunda ± musbat. 32 ni 2\sqrt{211} ga qo'shish.

$$x=\frac{2\sqrt{211}+32}{2}$$

32+2\sqrt{211} ni 2 ga bo'lish.

$$x=\sqrt{211}+16$$

x=\frac{32±2\sqrt{211}}{2} tenglamasini yeching, bunda ± manfiy. 32 dan 2\sqrt{211} ni ayirish.

$$x=\frac{32-2\sqrt{211}}{2}$$

32-2\sqrt{211} ni 2 ga bo'lish.

$$x=16-\sqrt{211}$$

Tenglama yechildi.

$$x=\sqrt{211}+16 x=16-\sqrt{211}$$

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.

$$x^{2}-32x+45=0$$

Tenglamaning ikkala tarafidan 45 ni ayirish.

$$x^{2}-32x+45-45=-45$$

O‘zidan 45 ayirilsa 0 qoladi.

$$x^{2}-32x=-45$$

-32 ni bo‘lish, x shartining koeffitsienti, 2 ga -16 olish uchun. Keyin, -16 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-32x+\left(-16\right)^{2}=-45+\left(-16\right)^{2}$$

-16 kvadratini chiqarish.

$$x^{2}-32x+256=-45+256$$

-45 ni 256 ga qo'shish.

$$x^{2}-32x+256=211$$

x^{2}-32x+256 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-16\right)^{2}=211$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-16\right)^{2}}=\sqrt{211}$$

Qisqartirish.

$$x-16=\sqrt{211} x-16=-\sqrt{211}$$

16 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{211}+16 x=16-\sqrt{211}$$