(384x-048)*(3x+4)=30 eching

$$(384x-048) \times (3x+4)=30$$

x uchun yechish

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3}\approx 0,019253235$$

$$x=-\frac{\sqrt{271}}{24}-\frac{2}{3}\approx -1,352586568$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 48 ni ko'paytirish.

$$\left(384x-0\right)\left(3x+4\right)=30$$

384x-0 ga 3x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3\left(384x-0\right)x+4\left(384x-0\right)=30$$

Ikkala tarafdan 30 ni ayirish.

$$3\left(384x-0\right)x+4\left(384x-0\right)-30=0$$

Shartlarni qayta saralash.

$$3\times 384xx+4\times 384x-30=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3\times 384x^{2}+4\times 384x-30=0$$

1152 hosil qilish uchun 3 va 384 ni ko'paytirish. 1536 hosil qilish uchun 4 va 384 ni ko'paytirish.

$$1152x^{2}+1536x-30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1152 ni a, 1536 ni b va -30 ni c bilan almashtiring.

$$x=\frac{-1536±\sqrt{1536^{2}-4\times 1152\left(-30\right)}}{2\times 1152}$$

1536 kvadratini chiqarish.

$$x=\frac{-1536±\sqrt{2359296-4\times 1152\left(-30\right)}}{2\times 1152}$$

-4 ni 1152 marotabaga ko'paytirish.

$$x=\frac{-1536±\sqrt{2359296-4608\left(-30\right)}}{2\times 1152}$$

-4608 ni -30 marotabaga ko'paytirish.

$$x=\frac{-1536±\sqrt{2359296+138240}}{2\times 1152}$$

2359296 ni 138240 ga qo'shish.

$$x=\frac{-1536±\sqrt{2497536}}{2\times 1152}$$

2497536 ning kvadrat ildizini chiqarish.

$$x=\frac{-1536±96\sqrt{271}}{2\times 1152}$$

2 ni 1152 marotabaga ko'paytirish.

$$x=\frac{-1536±96\sqrt{271}}{2304}$$

x=\frac{-1536±96\sqrt{271}}{2304} tenglamasini yeching, bunda ± musbat. -1536 ni 96\sqrt{271} ga qo'shish.

$$x=\frac{96\sqrt{271}-1536}{2304}$$

-1536+96\sqrt{271} ni 2304 ga bo'lish.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3}$$

x=\frac{-1536±96\sqrt{271}}{2304} tenglamasini yeching, bunda ± manfiy. -1536 dan 96\sqrt{271} ni ayirish.

$$x=\frac{-96\sqrt{271}-1536}{2304}$$

-1536-96\sqrt{271} ni 2304 ga bo'lish.

$$x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$

Tenglama yechildi.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3} x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 48 ni ko'paytirish.

$$\left(384x-0\right)\left(3x+4\right)=30$$

384x-0 ga 3x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3\left(384x-0\right)x+4\left(384x-0\right)=30$$

Shartlarni qayta saralash.

$$3\times 384xx+4\times 384x=30$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3\times 384x^{2}+4\times 384x=30$$

1152 hosil qilish uchun 3 va 384 ni ko'paytirish. 1536 hosil qilish uchun 4 va 384 ni ko'paytirish.

$$1152x^{2}+1536x=30$$

Ikki tarafini 1152 ga bo‘ling.

$$\frac{1152x^{2}+1536x}{1152}=\frac{30}{1152}$$

1152 ga bo'lish 1152 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1536}{1152}x=\frac{30}{1152}$$

\frac{1536}{1152} ulushini 384 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{4}{3}x=\frac{30}{1152}$$

\frac{30}{1152} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{4}{3}x=\frac{5}{192}$$

\frac{4}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{2}{3} olish uchun. Keyin, \frac{2}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{4}{3}x+\left(\frac{2}{3}\right)^{2}=\frac{5}{192}+\left(\frac{2}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{2}{3} kvadratini chiqarish.

$$x^{2}+\frac{4}{3}x+\frac{4}{9}=\frac{5}{192}+\frac{4}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{192} ni \frac{4}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{4}{3}x+\frac{4}{9}=\frac{271}{576}$$

x^{2}+\frac{4}{3}x+\frac{4}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{2}{3}\right)^{2}=\frac{271}{576}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{2}{3}\right)^{2}}=\sqrt{\frac{271}{576}}$$

Qisqartirish.

$$x+\frac{2}{3}=\frac{\sqrt{271}}{24} x+\frac{2}{3}=-\frac{\sqrt{271}}{24}$$

Tenglamaning ikkala tarafidan \frac{2}{3} ni ayirish.

$$x=\frac{\sqrt{271}}{24}-\frac{2}{3} x=-\frac{\sqrt{271}}{24}-\frac{2}{3}$$