2x/210-x=210-x/2x eching

$$\frac { 2 x } { 210 - x } = \frac { 210 - x } { 2 x }$$

x uchun yechish

$$x=-210$$

$$x=70$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,210 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x\left(x-210\right) ga, 210-x,2x ning eng kichik karralisiga ko‘paytiring.

$$-2x\times 2x=\left(x-210\right)\left(210-x\right)$$

-4 hosil qilish uchun -2 va 2 ni ko'paytirish.

$$-4xx=\left(x-210\right)\left(210-x\right)$$

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

$$-4x^{2}=\left(x-210\right)\left(210-x\right)$$

x-210 ga 210-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-4x^{2}=420x-x^{2}-44100$$

Ikkala tarafdan 420x ni ayirish.

$$-4x^{2}-420x=-x^{2}-44100$$

x^{2} ni ikki tarafga qo’shing.

$$-4x^{2}-420x+x^{2}=-44100$$

-3x^{2} ni olish uchun -4x^{2} va x^{2} ni birlashtirish.

$$-3x^{2}-420x=-44100$$

44100 ni ikki tarafga qo’shing.

$$-3x^{2}-420x+44100=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, -420 ni b va 44100 ni c bilan almashtiring.

$$x=\frac{-\left(-420\right)±\sqrt{\left(-420\right)^{2}-4\left(-3\right)\times 44100}}{2\left(-3\right)}$$

-420 kvadratini chiqarish.

$$x=\frac{-\left(-420\right)±\sqrt{176400-4\left(-3\right)\times 44100}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-420\right)±\sqrt{176400+12\times 44100}}{2\left(-3\right)}$$

12 ni 44100 marotabaga ko'paytirish.

$$x=\frac{-\left(-420\right)±\sqrt{176400+529200}}{2\left(-3\right)}$$

176400 ni 529200 ga qo'shish.

$$x=\frac{-\left(-420\right)±\sqrt{705600}}{2\left(-3\right)}$$

705600 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-420\right)±840}{2\left(-3\right)}$$

-420 ning teskarisi 420 ga teng.

$$x=\frac{420±840}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{420±840}{-6}$$

x=\frac{420±840}{-6} tenglamasini yeching, bunda ± musbat. 420 ni 840 ga qo'shish.

$$x=\frac{1260}{-6}$$

1260 ni -6 ga bo'lish.

$$x=-210$$

x=\frac{420±840}{-6} tenglamasini yeching, bunda ± manfiy. 420 dan 840 ni ayirish.

$$x=-\frac{420}{-6}$$

-420 ni -6 ga bo'lish.

$$x=70$$

Tenglama yechildi.

$$x=-210 x=70$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0,210 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x\left(x-210\right) ga, 210-x,2x ning eng kichik karralisiga ko‘paytiring.

$$-2x\times 2x=\left(x-210\right)\left(210-x\right)$$

-4 hosil qilish uchun -2 va 2 ni ko'paytirish.

$$-4xx=\left(x-210\right)\left(210-x\right)$$

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

$$-4x^{2}=\left(x-210\right)\left(210-x\right)$$

x-210 ga 210-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-4x^{2}=420x-x^{2}-44100$$

Ikkala tarafdan 420x ni ayirish.

$$-4x^{2}-420x=-x^{2}-44100$$

x^{2} ni ikki tarafga qo’shing.

$$-4x^{2}-420x+x^{2}=-44100$$

-3x^{2} ni olish uchun -4x^{2} va x^{2} ni birlashtirish.

$$-3x^{2}-420x=-44100$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}-420x}{-3}=-\frac{44100}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{420}{-3}\right)x=-\frac{44100}{-3}$$

-420 ni -3 ga bo'lish.

$$x^{2}+140x=-\frac{44100}{-3}$$

-44100 ni -3 ga bo'lish.

$$x^{2}+140x=14700$$

140 ni bo‘lish, x shartining koeffitsienti, 2 ga 70 olish uchun. Keyin, 70 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+140x+70^{2}=14700+70^{2}$$

70 kvadratini chiqarish.

$$x^{2}+140x+4900=14700+4900$$

14700 ni 4900 ga qo'shish.

$$x^{2}+140x+4900=19600$$

x^{2}+140x+4900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+70\right)^{2}=19600$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+70\right)^{2}}=\sqrt{19600}$$

Qisqartirish.

$$x+70=140 x+70=-140$$

Tenglamaning ikkala tarafidan 70 ni ayirish.

$$x=70 x=-210$$