4x^2-32x=0 eching

$$4 x ^ { 2 } - 32 x = 0$$

x uchun yechish

$$x=8$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(4x-32\right)=0$$

Tenglamani yechish uchun x=0 va 4x-32=0 ni yeching.

$$x=0 x=8$$

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.

$$4x^{2}-32x=0$$

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

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

\left(-32\right)^{2} ning kvadrat ildizini chiqarish.

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

-32 ning teskarisi 32 ga teng.

$$x=\frac{32±32}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{32±32}{8}$$

x=\frac{32±32}{8} tenglamasini yeching, bunda ± musbat. 32 ni 32 ga qo'shish.

$$x=\frac{64}{8}$$

64 ni 8 ga bo'lish.

$$x=8$$

x=\frac{32±32}{8} tenglamasini yeching, bunda ± manfiy. 32 dan 32 ni ayirish.

$$x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=8 x=0$$

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.

$$4x^{2}-32x=0$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-32x}{4}=\frac{0}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{32}{4}\right)x=\frac{0}{4}$$

-32 ni 4 ga bo'lish.

$$x^{2}-8x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x^{2}-8x=0$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=16$$

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-4\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-4=4 x-4=-4$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=8 x=0$$