-36x/-36+x=36+72x/72+x eching

$$\frac { - 36 x } { - 36 + x } = 36 + \frac { 72 x } { 72 + x }$$

x uchun yechish

$$x = \frac{9 \sqrt{33} - 9}{2} \approx 21,350531909$$

$$x=\frac{-9\sqrt{33}-9}{2}\approx -30,350531909$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -72,36 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-36\right)\left(x+72\right) ga, -36+x,72+x ning eng kichik karralisiga ko‘paytiring.

$$\left(x+72\right)\left(-36\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

x+72 ga -36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-36x-2592\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

-36x-2592 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

x-36 ga x+72 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-36x^{2}-2592x=\left(x^{2}+36x-2592\right)\times 36+\left(x-36\right)\times 72x$$

x^{2}+36x-2592 ga 36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+\left(x-36\right)\times 72x$$

x-36 ga 72 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+\left(72x-2592\right)x$$

72x-2592 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+72x^{2}-2592x$$

108x^{2} ni olish uchun 36x^{2} va 72x^{2} ni birlashtirish.

$$-36x^{2}-2592x=108x^{2}+1296x-93312-2592x$$

-1296x ni olish uchun 1296x va -2592x ni birlashtirish.

$$-36x^{2}-2592x=108x^{2}-1296x-93312$$

Ikkala tarafdan 108x^{2} ni ayirish.

$$-36x^{2}-2592x-108x^{2}=-1296x-93312$$

-144x^{2} ni olish uchun -36x^{2} va -108x^{2} ni birlashtirish.

$$-144x^{2}-2592x=-1296x-93312$$

1296x ni ikki tarafga qo’shing.

$$-144x^{2}-2592x+1296x=-93312$$

-1296x ni olish uchun -2592x va 1296x ni birlashtirish.

$$-144x^{2}-1296x=-93312$$

93312 ni ikki tarafga qo’shing.

$$-144x^{2}-1296x+93312=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -144 ni a, -1296 ni b va 93312 ni c bilan almashtiring.

$$x=\frac{-\left(-1296\right)±\sqrt{\left(-1296\right)^{2}-4\left(-144\right)\times 93312}}{2\left(-144\right)}$$

-1296 kvadratini chiqarish.

$$x=\frac{-\left(-1296\right)±\sqrt{1679616-4\left(-144\right)\times 93312}}{2\left(-144\right)}$$

-4 ni -144 marotabaga ko'paytirish.

$$x=\frac{-\left(-1296\right)±\sqrt{1679616+576\times 93312}}{2\left(-144\right)}$$

576 ni 93312 marotabaga ko'paytirish.

$$x=\frac{-\left(-1296\right)±\sqrt{1679616+53747712}}{2\left(-144\right)}$$

1679616 ni 53747712 ga qo'shish.

$$x=\frac{-\left(-1296\right)±\sqrt{55427328}}{2\left(-144\right)}$$

55427328 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1296\right)±1296\sqrt{33}}{2\left(-144\right)}$$

-1296 ning teskarisi 1296 ga teng.

$$x=\frac{1296±1296\sqrt{33}}{2\left(-144\right)}$$

2 ni -144 marotabaga ko'paytirish.

$$x=\frac{1296±1296\sqrt{33}}{-288}$$

x=\frac{1296±1296\sqrt{33}}{-288} tenglamasini yeching, bunda ± musbat. 1296 ni 1296\sqrt{33} ga qo'shish.

$$x=\frac{1296\sqrt{33}+1296}{-288}$$

1296+1296\sqrt{33} ni -288 ga bo'lish.

$$x=\frac{-9\sqrt{33}-9}{2}$$

x=\frac{1296±1296\sqrt{33}}{-288} tenglamasini yeching, bunda ± manfiy. 1296 dan 1296\sqrt{33} ni ayirish.

$$x=\frac{1296-1296\sqrt{33}}{-288}$$

1296-1296\sqrt{33} ni -288 ga bo'lish.

$$x=\frac{9\sqrt{33}-9}{2}$$

Tenglama yechildi.

$$x=\frac{-9\sqrt{33}-9}{2} x=\frac{9\sqrt{33}-9}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -72,36 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-36\right)\left(x+72\right) ga, -36+x,72+x ning eng kichik karralisiga ko‘paytiring.

$$\left(x+72\right)\left(-36\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

x+72 ga -36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-36x-2592\right)x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

-36x-2592 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=\left(x-36\right)\left(x+72\right)\times 36+\left(x-36\right)\times 72x$$

x-36 ga x+72 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-36x^{2}-2592x=\left(x^{2}+36x-2592\right)\times 36+\left(x-36\right)\times 72x$$

x^{2}+36x-2592 ga 36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+\left(x-36\right)\times 72x$$

x-36 ga 72 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+\left(72x-2592\right)x$$

72x-2592 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-36x^{2}-2592x=36x^{2}+1296x-93312+72x^{2}-2592x$$

108x^{2} ni olish uchun 36x^{2} va 72x^{2} ni birlashtirish.

$$-36x^{2}-2592x=108x^{2}+1296x-93312-2592x$$

-1296x ni olish uchun 1296x va -2592x ni birlashtirish.

$$-36x^{2}-2592x=108x^{2}-1296x-93312$$

Ikkala tarafdan 108x^{2} ni ayirish.

$$-36x^{2}-2592x-108x^{2}=-1296x-93312$$

-144x^{2} ni olish uchun -36x^{2} va -108x^{2} ni birlashtirish.

$$-144x^{2}-2592x=-1296x-93312$$

1296x ni ikki tarafga qo’shing.

$$-144x^{2}-2592x+1296x=-93312$$

-1296x ni olish uchun -2592x va 1296x ni birlashtirish.

$$-144x^{2}-1296x=-93312$$

Ikki tarafini -144 ga bo‘ling.

$$\frac{-144x^{2}-1296x}{-144}=-\frac{93312}{-144}$$

-144 ga bo'lish -144 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{1296}{-144}\right)x=-\frac{93312}{-144}$$

-1296 ni -144 ga bo'lish.

$$x^{2}+9x=-\frac{93312}{-144}$$

-93312 ni -144 ga bo'lish.

$$x^{2}+9x=648$$

9 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{2} olish uchun. Keyin, \frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=648+\left(\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{2} kvadratini chiqarish.

$$x^{2}+9x+\frac{81}{4}=648+\frac{81}{4}$$

648 ni \frac{81}{4} ga qo'shish.

$$x^{2}+9x+\frac{81}{4}=\frac{2673}{4}$$

x^{2}+9x+\frac{81}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{2673}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{2673}{4}}$$

Qisqartirish.

$$x+\frac{9}{2}=\frac{9\sqrt{33}}{2} x+\frac{9}{2}=-\frac{9\sqrt{33}}{2}$$

Tenglamaning ikkala tarafidan \frac{9}{2} ni ayirish.

$$x=\frac{9\sqrt{33}-9}{2} x=\frac{-9\sqrt{33}-9}{2}$$