7x^2-8x=0 eching

$$7 x ^ { 2 } - 8 x = 0$$

x uchun yechish

$$x = \frac{8}{7} = 1\frac{1}{7} \approx 1,142857143$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(7x-8\right)=0$$

Tenglamani yechish uchun x=0 va 7x-8=0 ni yeching.

$$x=0 x=\frac{8}{7}$$

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.

$$7x^{2}-8x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -8 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 7}$$

\left(-8\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±8}{2\times 7}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±8}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{8±8}{14}$$

x=\frac{8±8}{14} tenglamasini yeching, bunda ± musbat. 8 ni 8 ga qo'shish.

$$x=\frac{16}{14}$$

\frac{16}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{8}{7}$$

x=\frac{8±8}{14} tenglamasini yeching, bunda ± manfiy. 8 dan 8 ni ayirish.

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

0 ni 14 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{8}{7} x=0$$

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.

$$7x^{2}-8x=0$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-8x}{7}=\frac{0}{7}$$

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

$$x^{2}-\frac{8}{7}x=\frac{0}{7}$$

0 ni 7 ga bo'lish.

$$x^{2}-\frac{8}{7}x=0$$

-\frac{8}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4}{7} olish uchun. Keyin, -\frac{4}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{8}{7}x+\left(-\frac{4}{7}\right)^{2}=\left(-\frac{4}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4}{7} kvadratini chiqarish.

$$x^{2}-\frac{8}{7}x+\frac{16}{49}=\frac{16}{49}$$

x^{2}-\frac{8}{7}x+\frac{16}{49} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{4}{7}\right)^{2}=\frac{16}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{4}{7}\right)^{2}}=\sqrt{\frac{16}{49}}$$

Qisqartirish.

$$x-\frac{4}{7}=\frac{4}{7} x-\frac{4}{7}=-\frac{4}{7}$$

\frac{4}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{8}{7} x=0$$