(1215-x)*30000+30000=36790/x eching

$$( 1215 - x ) \times 30000 + 30000 = \frac { 36790 } { x }$$

x uchun yechish

$$x=\frac{\sqrt{33269649630}}{300}+608\approx 1215,998991501$$

$$x=-\frac{\sqrt{33269649630}}{300}+608\approx 0,001008499$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

1215-x ga 30000 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

36450000-30000x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36450000x-30000x^{2}+x\times 30000=36790$$

36480000x ni olish uchun 36450000x va x\times 30000 ni birlashtirish.

$$36480000x-30000x^{2}=36790$$

Ikkala tarafdan 36790 ni ayirish.

$$36480000x-30000x^{2}-36790=0$$

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.

$$-30000x^{2}[phone]x-36790=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -30000 ni a, 36480000 ni b va -36790 ni c bilan almashtiring.

$$x=\frac{-36480000±\sqrt{36480000^{2}-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

36480000 kvadratini chiqarish.

$$x=\frac{-36480000±\sqrt{1330790400000000-4\left(-30000\right)\left(-36790\right)}}{2\left(-30000\right)}$$

-4 ni -30000 marotabaga ko'paytirish.

$$x=\frac{-36480000±\sqrt{1330790400000000+120000\left(-36790\right)}}{2\left(-30000\right)}$$

120000 ni -36790 marotabaga ko'paytirish.

$$x=\frac{-36480000±\sqrt{1330790400000000-4414800000}}{2\left(-30000\right)}$$

1330790400000000 ni -4414800000 ga qo'shish.

$$x=\frac{-36480000±\sqrt{1330785985200000}}{2\left(-30000\right)}$$

1330785985200000 ning kvadrat ildizini chiqarish.

$$x=\frac{-36480000±200\sqrt{33269649630}}{2\left(-30000\right)}$$

2 ni -30000 marotabaga ko'paytirish.

$$x=\frac{-36480000±200\sqrt{33269649630}}{-60000}$$

x=\frac{-36480000±200\sqrt{33269649630}}{-60000} tenglamasini yeching, bunda ± musbat. -36480000 ni 200\sqrt{33269649630} ga qo'shish.

$$x=\frac{200\sqrt{33269649630}-36480000}{-60000}$$

-36480000+200\sqrt{33269649630} ni -60000 ga bo'lish.

$$x=-\frac{\sqrt{33269649630}}{300}+608$$

x=\frac{-36480000±200\sqrt{33269649630}}{-60000} tenglamasini yeching, bunda ± manfiy. -36480000 dan 200\sqrt{33269649630} ni ayirish.

$$x=\frac{-200\sqrt{33269649630}-36480000}{-60000}$$

-36480000-200\sqrt{33269649630} ni -60000 ga bo'lish.

$$x=\frac{\sqrt{33269649630}}{300}+608$$

Tenglama yechildi.

$$x=-\frac{\sqrt{33269649630}}{300}+608 x=\frac{\sqrt{33269649630}}{300}+608$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(1215-x\right)\times 30000x+x\times 30000=36790$$

1215-x ga 30000 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(36450000-30000x\right)x+x\times 30000=36790$$

36450000-30000x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36450000x-30000x^{2}+x\times 30000=36790$$

36480000x ni olish uchun 36450000x va x\times 30000 ni birlashtirish.

$$36480000x-30000x^{2}=36790$$

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

$$-30000x^{2}[phone]x=36790$$

Ikki tarafini -30000 ga bo‘ling.

$$\frac{-30000x^{2}[phone]x}{-30000}=\frac{36790}{-30000}$$

-30000 ga bo'lish -30000 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{36480000}{-30000}x=\frac{36790}{-30000}$$

36480000 ni -30000 ga bo'lish.

$$x^{2}-1216x=\frac{36790}{-30000}$$

\frac{36790}{-30000} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-1216x=-\frac{3679}{3000}$$

-1216 ni bo‘lish, x shartining koeffitsienti, 2 ga -608 olish uchun. Keyin, -608 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-1216x+\left(-608\right)^{2}=-\frac{3679}{3000}+\left(-608\right)^{2}$$

-608 kvadratini chiqarish.

$$x^{2}-1216x+369664=-\frac{3679}{3000}+369664$$

-\frac{3679}{3000} ni 369664 ga qo'shish.

$$x^{2}-1216x+369664=\frac{1108988321}{3000}$$

x^{2}-1216x+369664 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-608\right)^{2}=\frac{1108988321}{3000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-608\right)^{2}}=\sqrt{\frac{1108988321}{3000}}$$

Qisqartirish.

$$x-608=\frac{\sqrt{33269649630}}{300} x-608=-\frac{\sqrt{33269649630}}{300}$$

608 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{33269649630}}{300}+608 x=-\frac{\sqrt{33269649630}}{300}+608$$