7200(1+02)/x-7200/x+4=200 eching

$$\frac { 7200 ( 1 + 02 ) } { x } - \frac { 7200 } { x + 4 } = 200$$

x uchun yechish

$$x=2\sqrt{37}-2\approx 10,165525061$$

$$x=-2\sqrt{37}-2\approx -14,165525061$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -4,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+4\right) ga, x,x+4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+4\right)\times 7200\left(1+0\times 2\right)-x\times 7200=200x\left(x+4\right)$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\left(x+4\right)\times 7200\left(1+0\right)-x\times 7200=200x\left(x+4\right)$$

1 olish uchun 1 va 0'ni qo'shing.

$$\left(x+4\right)\times 7200\times 1-x\times 7200=200x\left(x+4\right)$$

7200 hosil qilish uchun 7200 va 1 ni ko'paytirish.

$$\left(x+4\right)\times 7200-x\times 7200=200x\left(x+4\right)$$

x+4 ga 7200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$7200x+28800-x\times 7200=200x\left(x+4\right)$$

200x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$7200x+28800-x\times 7200=200x^{2}+800x$$

Ikkala tarafdan 200x^{2} ni ayirish.

$$7200x+28800-x\times 7200-200x^{2}=800x$$

Ikkala tarafdan 800x ni ayirish.

$$7200x+28800-x\times 7200-200x^{2}-800x=0$$

6400x ni olish uchun 7200x va -800x ni birlashtirish.

$$6400x+28800-x\times 7200-200x^{2}=0$$

-7200 hosil qilish uchun -1 va 7200 ni ko'paytirish.

$$6400x+28800-7200x-200x^{2}=0$$

-800x ni olish uchun 6400x va -7200x ni birlashtirish.

$$-800x+28800-200x^{2}=0$$

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.

$$-200x^{2}-800x+28800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -200 ni a, -800 ni b va 28800 ni c bilan almashtiring.

$$x=\frac{-\left(-800\right)±\sqrt{\left(-800\right)^{2}-4\left(-200\right)\times 28800}}{2\left(-200\right)}$$

-800 kvadratini chiqarish.

$$x=\frac{-\left(-800\right)±\sqrt{640000-4\left(-200\right)\times 28800}}{2\left(-200\right)}$$

-4 ni -200 marotabaga ko'paytirish.

$$x=\frac{-\left(-800\right)±\sqrt{640000+800\times 28800}}{2\left(-200\right)}$$

800 ni 28800 marotabaga ko'paytirish.

$$x=\frac{-\left(-800\right)±\sqrt{640000+23040000}}{2\left(-200\right)}$$

640000 ni 23040000 ga qo'shish.

$$x=\frac{-\left(-800\right)±\sqrt{23680000}}{2\left(-200\right)}$$

23680000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-800\right)±800\sqrt{37}}{2\left(-200\right)}$$

-800 ning teskarisi 800 ga teng.

$$x=\frac{800±800\sqrt{37}}{2\left(-200\right)}$$

2 ni -200 marotabaga ko'paytirish.

$$x=\frac{800±800\sqrt{37}}{-400}$$

x=\frac{800±800\sqrt{37}}{-400} tenglamasini yeching, bunda ± musbat. 800 ni 800\sqrt{37} ga qo'shish.

$$x=\frac{800\sqrt{37}+800}{-400}$$

800+800\sqrt{37} ni -400 ga bo'lish.

$$x=-2\sqrt{37}-2$$

x=\frac{800±800\sqrt{37}}{-400} tenglamasini yeching, bunda ± manfiy. 800 dan 800\sqrt{37} ni ayirish.

$$x=\frac{800-800\sqrt{37}}{-400}$$

800-800\sqrt{37} ni -400 ga bo'lish.

$$x=2\sqrt{37}-2$$

Tenglama yechildi.

$$x=-2\sqrt{37}-2 x=2\sqrt{37}-2$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -4,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x+4\right) ga, x,x+4 ning eng kichik karralisiga ko‘paytiring.

$$\left(x+4\right)\times 7200\left(1+0\times 2\right)-x\times 7200=200x\left(x+4\right)$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\left(x+4\right)\times 7200\left(1+0\right)-x\times 7200=200x\left(x+4\right)$$

1 olish uchun 1 va 0'ni qo'shing.

$$\left(x+4\right)\times 7200\times 1-x\times 7200=200x\left(x+4\right)$$

7200 hosil qilish uchun 7200 va 1 ni ko'paytirish.

$$\left(x+4\right)\times 7200-x\times 7200=200x\left(x+4\right)$$

x+4 ga 7200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$7200x+28800-x\times 7200=200x\left(x+4\right)$$

200x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$7200x+28800-x\times 7200=200x^{2}+800x$$

Ikkala tarafdan 200x^{2} ni ayirish.

$$7200x+28800-x\times 7200-200x^{2}=800x$$

Ikkala tarafdan 800x ni ayirish.

$$7200x+28800-x\times 7200-200x^{2}-800x=0$$

6400x ni olish uchun 7200x va -800x ni birlashtirish.

$$6400x+28800-x\times 7200-200x^{2}=0$$

Ikkala tarafdan 28800 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$6400x-x\times 7200-200x^{2}=-28800$$

-7200 hosil qilish uchun -1 va 7200 ni ko'paytirish.

$$6400x-7200x-200x^{2}=-28800$$

-800x ni olish uchun 6400x va -7200x ni birlashtirish.

$$-800x-200x^{2}=-28800$$

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

$$-200x^{2}-800x=-28800$$

Ikki tarafini -200 ga bo‘ling.

$$\frac{-200x^{2}-800x}{-200}=-\frac{28800}{-200}$$

-200 ga bo'lish -200 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{800}{-200}\right)x=-\frac{28800}{-200}$$

-800 ni -200 ga bo'lish.

$$x^{2}+4x=-\frac{28800}{-200}$$

-28800 ni -200 ga bo'lish.

$$x^{2}+4x=144$$

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

$$x^{2}+4x+2^{2}=144+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=144+4$$

144 ni 4 ga qo'shish.

$$x^{2}+4x+4=148$$

x^{2}+4x+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.

$$\left(x+2\right)^{2}=148$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{148}$$

Qisqartirish.

$$x+2=2\sqrt{37} x+2=-2\sqrt{37}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=2\sqrt{37}-2 x=-2\sqrt{37}-2$$