(72-2x)(48-2x)=2160 eching

$$(72-2x)(48-2x)=2160$$

x uchun yechish

$$x=54$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

72-2x ga 48-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3456-240x+4x^{2}=2160$$

Ikkala tarafdan 2160 ni ayirish.

$$3456-240x+4x^{2}-2160=0$$

1296 olish uchun 3456 dan 2160 ni ayirish.

$$1296-240x+4x^{2}=0$$

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.

$$4x^{2}-240x+1296=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -240 ni b va 1296 ni c bilan almashtiring.

$$x=\frac{-\left(-240\right)±\sqrt{\left(-240\right)^{2}-4\times 4\times 1296}}{2\times 4}$$

-240 kvadratini chiqarish.

$$x=\frac{-\left(-240\right)±\sqrt{57600-4\times 4\times 1296}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-240\right)±\sqrt{57600-16\times 1296}}{2\times 4}$$

-16 ni 1296 marotabaga ko'paytirish.

$$x=\frac{-\left(-240\right)±\sqrt{57600-20736}}{2\times 4}$$

57600 ni -20736 ga qo'shish.

$$x=\frac{-\left(-240\right)±\sqrt{36864}}{2\times 4}$$

36864 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-240\right)±192}{2\times 4}$$

-240 ning teskarisi 240 ga teng.

$$x=\frac{240±192}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{240±192}{8}$$

x=\frac{240±192}{8} tenglamasini yeching, bunda ± musbat. 240 ni 192 ga qo'shish.

$$x=\frac{432}{8}$$

432 ni 8 ga bo'lish.

$$x=54$$

x=\frac{240±192}{8} tenglamasini yeching, bunda ± manfiy. 240 dan 192 ni ayirish.

$$x=\frac{48}{8}$$

48 ni 8 ga bo'lish.

$$x=6$$

Tenglama yechildi.

$$x=54 x=6$$

Kvadratni yakunlash bo'yicha qadamlar

72-2x ga 48-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3456-240x+4x^{2}=2160$$

Ikkala tarafdan 3456 ni ayirish.

$$-240x+4x^{2}=2160-3456$$

-1296 olish uchun 2160 dan 3456 ni ayirish.

$$-240x+4x^{2}=-1296$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$4x^{2}-240x=-1296$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-240x}{4}=-\frac{1296}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{240}{4}\right)x=-\frac{1296}{4}$$

-240 ni 4 ga bo'lish.

$$x^{2}-60x=-\frac{1296}{4}$$

-1296 ni 4 ga bo'lish.

$$x^{2}-60x=-324$$

-60 ni bo‘lish, x shartining koeffitsienti, 2 ga -30 olish uchun. Keyin, -30 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-60x+\left(-30\right)^{2}=-324+\left(-30\right)^{2}$$

-30 kvadratini chiqarish.

$$x^{2}-60x+900=-324+900$$

-324 ni 900 ga qo'shish.

$$x^{2}-60x+900=576$$

x^{2}-60x+900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-30\right)^{2}=576$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{576}$$

Qisqartirish.

$$x-30=24 x-30=-24$$

30 ni tenglamaning ikkala tarafiga qo'shish.

$$x=54 x=6$$