28x^2+7x=0 eching

$$28 x ^ { 2 } + 7 x = 0$$

x uchun yechish

$$x=-\frac{1}{4}=-0,25$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(28x+7\right)=0$$

Tenglamani yechish uchun x=0 va 28x+7=0 ni yeching.

$$x=0 x=-\frac{1}{4}$$

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.

$$28x^{2}+7x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 28 ni a, 7 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}}}{2\times 28}$$

7^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-7±7}{2\times 28}$$

2 ni 28 marotabaga ko'paytirish.

$$x=\frac{-7±7}{56}$$

x=\frac{-7±7}{56} tenglamasini yeching, bunda ± musbat. -7 ni 7 ga qo'shish.

$$x=\frac{0}{56}$$

0 ni 56 ga bo'lish.

$$x=0$$

x=\frac{-7±7}{56} tenglamasini yeching, bunda ± manfiy. -7 dan 7 ni ayirish.

$$x=-\frac{14}{56}$$

\frac{-14}{56} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{4}$$

Tenglama yechildi.

$$x=0 x=-\frac{1}{4}$$

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.

$$28x^{2}+7x=0$$

Ikki tarafini 28 ga bo‘ling.

$$\frac{28x^{2}+7x}{28}=\frac{0}{28}$$

28 ga bo'lish 28 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{28}x=\frac{0}{28}$$

\frac{7}{28} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{4}x=\frac{0}{28}$$

0 ni 28 ga bo'lish.

$$x^{2}+\frac{1}{4}x=0$$

\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{8} olish uchun. Keyin, \frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=\left(\frac{1}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{8} kvadratini chiqarish.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{1}{64}$$

x^{2}+\frac{1}{4}x+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Qisqartirish.

$$x+\frac{1}{8}=\frac{1}{8} x+\frac{1}{8}=-\frac{1}{8}$$

Tenglamaning ikkala tarafidan \frac{1}{8} ni ayirish.

$$x=0 x=-\frac{1}{4}$$