04+20/10=120/x+120/x+10 eching

$$04 + \frac { 20 } { 10 } = \frac { 120 } { x } + \frac { 120 } { x + 10 }$$

x uchun yechish

$$x=5\sqrt{145}+55\approx 115,207972894$$

$$x=55-5\sqrt{145}\approx -5,207972894$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -10,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10x\left(x+10\right) ga, 10,x,x+10 ning eng kichik karralisiga ko‘paytiring.

$$0\times 4\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

0 hosil qilish uchun 0 va 4 ni ko'paytirish.

$$0\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

0 hosil qilish uchun 0 va 10 ni ko'paytirish.

$$0x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$0+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

x ga x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0+\left(x^{2}+10x\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

x^{2}+10x ga 20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0+20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

10x+100 ga 120 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x^{2}+200x=1200x+12000+10x\times 120$$

1200 hosil qilish uchun 10 va 120 ni ko'paytirish.

$$20x^{2}+200x=1200x+12000+1200x$$

2400x ni olish uchun 1200x va 1200x ni birlashtirish.

$$20x^{2}+200x=2400x+12000$$

Ikkala tarafdan 2400x ni ayirish.

$$20x^{2}+200x-2400x=12000$$

-2200x ni olish uchun 200x va -2400x ni birlashtirish.

$$20x^{2}-2200x=12000$$

Ikkala tarafdan 12000 ni ayirish.

$$20x^{2}-2200x-12000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 20 ni a, -2200 ni b va -12000 ni c bilan almashtiring.

$$x=\frac{-\left(-2200\right)±\sqrt{\left(-2200\right)^{2}-4\times 20\left(-12000\right)}}{2\times 20}$$

-2200 kvadratini chiqarish.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000-4\times 20\left(-12000\right)}}{2\times 20}$$

-4 ni 20 marotabaga ko'paytirish.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000-80\left(-12000\right)}}{2\times 20}$$

-80 ni -12000 marotabaga ko'paytirish.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000+960000}}{2\times 20}$$

4840000 ni 960000 ga qo'shish.

$$x=\frac{-\left(-2200\right)±\sqrt{5800000}}{2\times 20}$$

5800000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2200\right)±200\sqrt{145}}{2\times 20}$$

-2200 ning teskarisi 2200 ga teng.

$$x=\frac{2200±200\sqrt{145}}{2\times 20}$$

2 ni 20 marotabaga ko'paytirish.

$$x=\frac{2200±200\sqrt{145}}{40}$$

x=\frac{2200±200\sqrt{145}}{40} tenglamasini yeching, bunda ± musbat. 2200 ni 200\sqrt{145} ga qo'shish.

$$x=\frac{200\sqrt{145}+2200}{40}$$

2200+200\sqrt{145} ni 40 ga bo'lish.

$$x=5\sqrt{145}+55$$

x=\frac{2200±200\sqrt{145}}{40} tenglamasini yeching, bunda ± manfiy. 2200 dan 200\sqrt{145} ni ayirish.

$$x=\frac{2200-200\sqrt{145}}{40}$$

2200-200\sqrt{145} ni 40 ga bo'lish.

$$x=55-5\sqrt{145}$$

Tenglama yechildi.

$$x=5\sqrt{145}+55 x=55-5\sqrt{145}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -10,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10x\left(x+10\right) ga, 10,x,x+10 ning eng kichik karralisiga ko‘paytiring.

$$0\times 4\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

0 hosil qilish uchun 0 va 4 ni ko'paytirish.

$$0\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

0 hosil qilish uchun 0 va 10 ni ko'paytirish.

$$0x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$0+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

x ga x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0+\left(x^{2}+10x\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

x^{2}+10x ga 20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0+20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

10x+100 ga 120 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x^{2}+200x=1200x+12000+10x\times 120$$

1200 hosil qilish uchun 10 va 120 ni ko'paytirish.

$$20x^{2}+200x=1200x+12000+1200x$$

2400x ni olish uchun 1200x va 1200x ni birlashtirish.

$$20x^{2}+200x=2400x+12000$$

Ikkala tarafdan 2400x ni ayirish.

$$20x^{2}+200x-2400x=12000$$

-2200x ni olish uchun 200x va -2400x ni birlashtirish.

$$20x^{2}-2200x=12000$$

Ikki tarafini 20 ga bo‘ling.

$$\frac{20x^{2}-2200x}{20}=\frac{12000}{20}$$

20 ga bo'lish 20 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{2200}{20}\right)x=\frac{12000}{20}$$

-2200 ni 20 ga bo'lish.

$$x^{2}-110x=\frac{12000}{20}$$

12000 ni 20 ga bo'lish.

$$x^{2}-110x=600$$

-110 ni bo‘lish, x shartining koeffitsienti, 2 ga -55 olish uchun. Keyin, -55 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-110x+\left(-55\right)^{2}=600+\left(-55\right)^{2}$$

-55 kvadratini chiqarish.

$$x^{2}-110x+3025=600+3025$$

600 ni 3025 ga qo'shish.

$$x^{2}-110x+3025=3625$$

x^{2}-110x+3025 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-55\right)^{2}=3625$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-55\right)^{2}}=\sqrt{3625}$$

Qisqartirish.

$$x-55=5\sqrt{145} x-55=-5\sqrt{145}$$

55 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5\sqrt{145}+55 x=55-5\sqrt{145}$$