4x(x+5)=6x-4x^2 eching

$$4 x ( x + 5 ) = 6 x - 4 x ^ { 2 }$$

x uchun yechish

$$x = -\frac{7}{4} = -1\frac{3}{4} = -1,75$$

$$x=0$$

Faktorlash qadamlari

4x ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+20x=6x-4x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$4x^{2}+20x-6x=-4x^{2}$$

14x ni olish uchun 20x va -6x ni birlashtirish.

$$4x^{2}+14x=-4x^{2}$$

4x^{2} ni ikki tarafga qo’shing.

$$4x^{2}+14x+4x^{2}=0$$

8x^{2} ni olish uchun 4x^{2} va 4x^{2} ni birlashtirish.

$$8x^{2}+14x=0$$

x omili.

$$x\left(8x+14\right)=0$$

Tenglamani yechish uchun x=0 va 8x+14=0 ni yeching.

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

Kvadrat tenglamalaridan foydalanish qoidalari

4x ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+20x=6x-4x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$4x^{2}+20x-6x=-4x^{2}$$

14x ni olish uchun 20x va -6x ni birlashtirish.

$$4x^{2}+14x=-4x^{2}$$

4x^{2} ni ikki tarafga qo’shing.

$$4x^{2}+14x+4x^{2}=0$$

8x^{2} ni olish uchun 4x^{2} va 4x^{2} ni birlashtirish.

$$8x^{2}+14x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 14 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-14±\sqrt{14^{2}}}{2\times 8}$$

14^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-14±14}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-14±14}{16}$$

x=\frac{-14±14}{16} tenglamasini yeching, bunda ± musbat. -14 ni 14 ga qo'shish.

$$x=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$x=0$$

x=\frac{-14±14}{16} tenglamasini yeching, bunda ± manfiy. -14 dan 14 ni ayirish.

$$x=-\frac{28}{16}$$

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

4x ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+20x=6x-4x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$4x^{2}+20x-6x=-4x^{2}$$

14x ni olish uchun 20x va -6x ni birlashtirish.

$$4x^{2}+14x=-4x^{2}$$

4x^{2} ni ikki tarafga qo’shing.

$$4x^{2}+14x+4x^{2}=0$$

8x^{2} ni olish uchun 4x^{2} va 4x^{2} ni birlashtirish.

$$8x^{2}+14x=0$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}+14x}{8}=\frac{0}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{14}{8}x=\frac{0}{8}$$

\frac{14}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{7}{4}x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{8} kvadratini chiqarish.

$$x^{2}+\frac{7}{4}x+\frac{49}{64}=\frac{49}{64}$$

x^{2}+\frac{7}{4}x+\frac{49}{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.

$$\left(x+\frac{7}{8}\right)^{2}=\frac{49}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{8}\right)^{2}}=\sqrt{\frac{49}{64}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{7}{8} ni ayirish.

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