5x^2-4*8x=0 eching

$$5 x ^ { 2 } - 4 \cdot 8 x = 0$$

x uchun yechish

$$x = \frac{32}{5} = 6\frac{2}{5} = 6,4$$

$$x=0$$

Faktorlash qadamlari

32 hosil qilish uchun 4 va 8 ni ko'paytirish.

$$5x^{2}-32x=0$$

x omili.

$$x\left(5x-32\right)=0$$

Tenglamani yechish uchun x=0 va 5x-32=0 ni yeching.

$$x=0 x=\frac{32}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

32 hosil qilish uchun 4 va 8 ni ko'paytirish.

$$5x^{2}-32x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -32 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}}}{2\times 5}$$

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

$$x=\frac{-\left(-32\right)±32}{2\times 5}$$

-32 ning teskarisi 32 ga teng.

$$x=\frac{32±32}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{32±32}{10}$$

x=\frac{32±32}{10} tenglamasini yeching, bunda ± musbat. 32 ni 32 ga qo'shish.

$$x=\frac{64}{10}$$

\frac{64}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{32}{5}$$

x=\frac{32±32}{10} tenglamasini yeching, bunda ± manfiy. 32 dan 32 ni ayirish.

$$x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{32}{5} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

32 hosil qilish uchun 4 va 8 ni ko'paytirish.

$$5x^{2}-32x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-32x}{5}=\frac{0}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{32}{5}x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}-\frac{32}{5}x=0$$

-\frac{32}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{16}{5} olish uchun. Keyin, -\frac{16}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{32}{5}x+\left(-\frac{16}{5}\right)^{2}=\left(-\frac{16}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{16}{5} kvadratini chiqarish.

$$x^{2}-\frac{32}{5}x+\frac{256}{25}=\frac{256}{25}$$

x^{2}-\frac{32}{5}x+\frac{256}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{16}{5}\right)^{2}=\frac{256}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{16}{5}\right)^{2}}=\sqrt{\frac{256}{25}}$$

Qisqartirish.

$$x-\frac{16}{5}=\frac{16}{5} x-\frac{16}{5}=-\frac{16}{5}$$

\frac{16}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{32}{5} x=0$$