7xx-5x=0 eching

$$7 x x - 5 x = 0$$

x uchun yechish

$$x=\frac{5}{7}\approx 0,714285714$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(7x-5\right)=0$$

Tenglamani yechish uchun x=0 va 7x-5=0 ni yeching.

$$x=0 x=\frac{5}{7}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$7x^{2}-5x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -5 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 7}$$

\left(-5\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±5}{2\times 7}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±5}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{5±5}{14}$$

x=\frac{5±5}{14} tenglamasini yeching, bunda ± musbat. 5 ni 5 ga qo'shish.

$$x=\frac{10}{14}$$

\frac{10}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{7}$$

x=\frac{5±5}{14} tenglamasini yeching, bunda ± manfiy. 5 dan 5 ni ayirish.

$$x=\frac{0}{14}$$

0 ni 14 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{5}{7} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$7x^{2}-5x=0$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-5x}{7}=\frac{0}{7}$$

7 ga bo'lish 7 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{5}{7}x=\frac{0}{7}$$

0 ni 7 ga bo'lish.

$$x^{2}-\frac{5}{7}x=0$$

-\frac{5}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{14} olish uchun. Keyin, -\frac{5}{14} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{7}x+\left(-\frac{5}{14}\right)^{2}=\left(-\frac{5}{14}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{14} kvadratini chiqarish.

$$x^{2}-\frac{5}{7}x+\frac{25}{196}=\frac{25}{196}$$

x^{2}-\frac{5}{7}x+\frac{25}{196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{5}{14}\right)^{2}=\frac{25}{196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{14}\right)^{2}}=\sqrt{\frac{25}{196}}$$

Qisqartirish.

$$x-\frac{5}{14}=\frac{5}{14} x-\frac{5}{14}=-\frac{5}{14}$$

\frac{5}{14} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5}{7} x=0$$