x^2-32x-32=0 eching

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

x uchun yechish

$$x=12\sqrt{2}+16\approx 32,970562748$$

$$x=16-12\sqrt{2}\approx -0,970562748$$

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.

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

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 -32 ni c bilan almashtiring.

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

-32 kvadratini chiqarish.

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

-4 ni -32 marotabaga ko'paytirish.

$$x=\frac{-\left(-32\right)±\sqrt{1024+128}}{2}$$

1024 ni 128 ga qo'shish.

$$x=\frac{-\left(-32\right)±\sqrt{1152}}{2}$$

1152 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-32\right)±24\sqrt{2}}{2}$$

-32 ning teskarisi 32 ga teng.

$$x=\frac{32±24\sqrt{2}}{2}$$

x=\frac{32±24\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 32 ni 24\sqrt{2} ga qo'shish.

$$x=\frac{24\sqrt{2}+32}{2}$$

32+24\sqrt{2} ni 2 ga bo'lish.

$$x=12\sqrt{2}+16$$

x=\frac{32±24\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 32 dan 24\sqrt{2} ni ayirish.

$$x=\frac{32-24\sqrt{2}}{2}$$

32-24\sqrt{2} ni 2 ga bo'lish.

$$x=16-12\sqrt{2}$$

Tenglama yechildi.

$$x=12\sqrt{2}+16 x=16-12\sqrt{2}$$

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.

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

32 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -32 ayirilsa 0 qoladi.

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

0 dan -32 ni ayirish.

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

-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.

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

-16 kvadratini chiqarish.

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

32 ni 256 ga qo'shish.

$$x^{2}-32x+256=288$$

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.

$$\left(x-16\right)^{2}=288$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-16\right)^{2}}=\sqrt{288}$$

Qisqartirish.

$$x-16=12\sqrt{2} x-16=-12\sqrt{2}$$

16 ni tenglamaning ikkala tarafiga qo'shish.

$$x=12\sqrt{2}+16 x=16-12\sqrt{2}$$