left(7xright)^2-14x=0 eching

$${ \left(7x \right) }^{ 2 } -14x = 0$$

x uchun yechish

$$x=\frac{2}{7}\approx 0,285714286$$

$$x=0$$

Faktorlash qadamlari

\left(7x\right)^{2} ni kengaytirish.

$$7^{2}x^{2}-14x=0$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49x^{2}-14x=0$$

x omili.

$$x\left(49x-14\right)=0$$

Tenglamani yechish uchun x=0 va 49x-14=0 ni yeching.

$$x=0 x=\frac{2}{7}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(7x\right)^{2} ni kengaytirish.

$$7^{2}x^{2}-14x=0$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49x^{2}-14x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 49 ni a, -14 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}}}{2\times 49}$$

\left(-14\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-14\right)±14}{2\times 49}$$

-14 ning teskarisi 14 ga teng.

$$x=\frac{14±14}{2\times 49}$$

2 ni 49 marotabaga ko'paytirish.

$$x=\frac{14±14}{98}$$

x=\frac{14±14}{98} tenglamasini yeching, bunda ± musbat. 14 ni 14 ga qo'shish.

$$x=\frac{28}{98}$$

\frac{28}{98} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{2}{7}$$

x=\frac{14±14}{98} tenglamasini yeching, bunda ± manfiy. 14 dan 14 ni ayirish.

$$x=\frac{0}{98}$$

0 ni 98 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{2}{7} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

\left(7x\right)^{2} ni kengaytirish.

$$7^{2}x^{2}-14x=0$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49x^{2}-14x=0$$

Ikki tarafini 49 ga bo‘ling.

$$\frac{49x^{2}-14x}{49}=\frac{0}{49}$$

49 ga bo'lish 49 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{14}{49}\right)x=\frac{0}{49}$$

\frac{-14}{49} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{2}{7}x=\frac{0}{49}$$

0 ni 49 ga bo'lish.

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

-\frac{2}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{7} olish uchun. Keyin, -\frac{1}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{2}{7}x+\left(-\frac{1}{7}\right)^{2}=\left(-\frac{1}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{7} kvadratini chiqarish.

$$x^{2}-\frac{2}{7}x+\frac{1}{49}=\frac{1}{49}$$

x^{2}-\frac{2}{7}x+\frac{1}{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.

$$\left(x-\frac{1}{7}\right)^{2}=\frac{1}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{7}\right)^{2}}=\sqrt{\frac{1}{49}}$$

Qisqartirish.

$$x-\frac{1}{7}=\frac{1}{7} x-\frac{1}{7}=-\frac{1}{7}$$

\frac{1}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{2}{7} x=0$$