-28x^2-16x=0 eching

$$- 28 x ^ { 2 } - 16 x = 0$$

x uchun yechish

$$x=-\frac{4}{7}\approx -0,571428571$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(-28x-16\right)=0$$

Tenglamani yechish uchun x=0 va -28x-16=0 ni yeching.

$$x=0 x=-\frac{4}{7}$$

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.

$$-28x^{2}-16x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -28 ni a, -16 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2\left(-28\right)}$$

\left(-16\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±16}{2\left(-28\right)}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±16}{2\left(-28\right)}$$

2 ni -28 marotabaga ko'paytirish.

$$x=\frac{16±16}{-56}$$

x=\frac{16±16}{-56} tenglamasini yeching, bunda ± musbat. 16 ni 16 ga qo'shish.

$$x=\frac{32}{-56}$$

\frac{32}{-56} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{16±16}{-56} tenglamasini yeching, bunda ± manfiy. 16 dan 16 ni ayirish.

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

0 ni -56 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{4}{7} x=0$$

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.

$$-28x^{2}-16x=0$$

Ikki tarafini -28 ga bo‘ling.

$$\frac{-28x^{2}-16x}{-28}=\frac{0}{-28}$$

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

$$x^{2}+\left(-\frac{16}{-28}\right)x=\frac{0}{-28}$$

\frac{-16}{-28} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{4}{7}x=\frac{0}{-28}$$

0 ni -28 ga bo'lish.

$$x^{2}+\frac{4}{7}x=0$$

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{2}{7} kvadratini chiqarish.

$$x^{2}+\frac{4}{7}x+\frac{4}{49}=\frac{4}{49}$$

x^{2}+\frac{4}{7}x+\frac{4}{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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{2}{7} ni ayirish.

$$x=0 x=-\frac{4}{7}$$