520div(x+10)+1=520+x eching

$$520 \div (x+10)+1=520+x$$

x uchun yechish

$$x=\frac{\sqrt{261161}-529}{2}\approx -8,980431278$$

$$x=\frac{-\sqrt{261161}-529}{2}\approx -520,019568722$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -10 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+10 ga ko'paytirish.

$$520+x+10=\left(x+10\right)\times 520+\left(x+10\right)x$$

530 olish uchun 520 va 10'ni qo'shing.

$$530+x=\left(x+10\right)\times 520+\left(x+10\right)x$$

x+10 ga 520 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$530+x=520x+5200+\left(x+10\right)x$$

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

$$530+x=520x+5200+x^{2}+10x$$

530x ni olish uchun 520x va 10x ni birlashtirish.

$$530+x=530x+5200+x^{2}$$

Ikkala tarafdan 530x ni ayirish.

$$530+x-530x=5200+x^{2}$$

-529x ni olish uchun x va -530x ni birlashtirish.

$$530-529x=5200+x^{2}$$

Ikkala tarafdan 5200 ni ayirish.

$$530-529x-5200=x^{2}$$

-4670 olish uchun 530 dan 5200 ni ayirish.

$$-4670-529x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-4670-529x-x^{2}=0$$

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.

$$-x^{2}-529x-4670=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -529 ni b va -4670 ni c bilan almashtiring.

$$x=\frac{-\left(-529\right)±\sqrt{\left(-529\right)^{2}-4\left(-1\right)\left(-4670\right)}}{2\left(-1\right)}$$

-529 kvadratini chiqarish.

$$x=\frac{-\left(-529\right)±\sqrt{279841-4\left(-1\right)\left(-4670\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-529\right)±\sqrt{279841+4\left(-4670\right)}}{2\left(-1\right)}$$

4 ni -4670 marotabaga ko'paytirish.

$$x=\frac{-\left(-529\right)±\sqrt{279841-18680}}{2\left(-1\right)}$$

279841 ni -18680 ga qo'shish.

$$x=\frac{-\left(-529\right)±\sqrt{261161}}{2\left(-1\right)}$$

-529 ning teskarisi 529 ga teng.

$$x=\frac{529±\sqrt{261161}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{529±\sqrt{261161}}{-2}$$

x=\frac{529±\sqrt{261161}}{-2} tenglamasini yeching, bunda ± musbat. 529 ni \sqrt{261161} ga qo'shish.

$$x=\frac{\sqrt{261161}+529}{-2}$$

529+\sqrt{261161} ni -2 ga bo'lish.

$$x=\frac{-\sqrt{261161}-529}{2}$$

x=\frac{529±\sqrt{261161}}{-2} tenglamasini yeching, bunda ± manfiy. 529 dan \sqrt{261161} ni ayirish.

$$x=\frac{529-\sqrt{261161}}{-2}$$

529-\sqrt{261161} ni -2 ga bo'lish.

$$x=\frac{\sqrt{261161}-529}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{261161}-529}{2} x=\frac{\sqrt{261161}-529}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -10 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+10 ga ko'paytirish.

$$520+x+10=\left(x+10\right)\times 520+\left(x+10\right)x$$

530 olish uchun 520 va 10'ni qo'shing.

$$530+x=\left(x+10\right)\times 520+\left(x+10\right)x$$

x+10 ga 520 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$530+x=520x+5200+\left(x+10\right)x$$

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

$$530+x=520x+5200+x^{2}+10x$$

530x ni olish uchun 520x va 10x ni birlashtirish.

$$530+x=530x+5200+x^{2}$$

Ikkala tarafdan 530x ni ayirish.

$$530+x-530x=5200+x^{2}$$

-529x ni olish uchun x va -530x ni birlashtirish.

$$530-529x=5200+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$530-529x-x^{2}=5200$$

Ikkala tarafdan 530 ni ayirish.

$$-529x-x^{2}=5200-530$$

4670 olish uchun 5200 dan 530 ni ayirish.

$$-529x-x^{2}=4670$$

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

$$-x^{2}-529x=4670$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-529x}{-1}=\frac{4670}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{529}{-1}\right)x=\frac{4670}{-1}$$

-529 ni -1 ga bo'lish.

$$x^{2}+529x=\frac{4670}{-1}$$

4670 ni -1 ga bo'lish.

$$x^{2}+529x=-4670$$

529 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{529}{2} olish uchun. Keyin, \frac{529}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+529x+\left(\frac{529}{2}\right)^{2}=-4670+\left(\frac{529}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{529}{2} kvadratini chiqarish.

$$x^{2}+529x+\frac{279841}{4}=-4670+\frac{279841}{4}$$

-4670 ni \frac{279841}{4} ga qo'shish.

$$x^{2}+529x+\frac{279841}{4}=\frac{261161}{4}$$

x^{2}+529x+\frac{279841}{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.

$$\left(x+\frac{529}{2}\right)^{2}=\frac{261161}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{529}{2}\right)^{2}}=\sqrt{\frac{261161}{4}}$$

Qisqartirish.

$$x+\frac{529}{2}=\frac{\sqrt{261161}}{2} x+\frac{529}{2}=-\frac{\sqrt{261161}}{2}$$

Tenglamaning ikkala tarafidan \frac{529}{2} ni ayirish.

$$x=\frac{\sqrt{261161}-529}{2} x=\frac{-\sqrt{261161}-529}{2}$$