24*10^8=039+x/(027-x)(043-x) eching

$$24 \times { 10 }^{ 8 } = \frac{ 039+x }{ (027-x)(043-x) }$$

x uchun yechish

$$x=\frac{1}{2400000000}\approx 4,166666667 \cdot 10^{-10}$$

Faktorlash qadamlari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$24\times 10^{8}x^{2}=0\times 39+x$$

8 daraja ko‘rsatkichini 10 ga hisoblang va 100000000 ni qiymatni oling.

$$24\times 100000000x^{2}=0\times 39+x$$

2400000000 hosil qilish uchun 24 va 100000000 ni ko'paytirish.

$$2400000000x^{2}=0\times 39+x$$

0 hosil qilish uchun 0 va 39 ni ko'paytirish.

$$2400000000x^{2}=0+x$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2400000000x^{2}=x$$

Ikkala tarafdan x ni ayirish.

$$2400000000x^{2}-x=0$$

x omili.

$$x\left(2400000000x-1\right)=0$$

Tenglamani yechish uchun x=0 va 2400000000x-1=0 ni yeching.

$$x=0 x=\frac{1}{2400000000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{1}{2400000000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$24\times 10^{8}x^{2}=0\times 39+x$$

8 daraja ko‘rsatkichini 10 ga hisoblang va 100000000 ni qiymatni oling.

$$24\times 100000000x^{2}=0\times 39+x$$

2400000000 hosil qilish uchun 24 va 100000000 ni ko'paytirish.

$$2400000000x^{2}=0\times 39+x$$

0 hosil qilish uchun 0 va 39 ni ko'paytirish.

$$2400000000x^{2}=0+x$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2400000000x^{2}=x$$

Ikkala tarafdan x ni ayirish.

$$2400000000x^{2}-x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2400000000 ni a, -1 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 2400000000}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2\times 2400000000}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2\times 2400000000}$$

2 ni 2400000000 marotabaga ko'paytirish.

$$x=\frac{1±1}{4800000000}$$

x=\frac{1±1}{4800000000} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$x=\frac{2}{4800000000}$$

\frac{2}{4800000000} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2400000000}$$

x=\frac{1±1}{4800000000} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

$$x=\frac{0}{4800000000}$$

0 ni 4800000000 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{2400000000} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{1}{2400000000}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$24\times 10^{8}x^{2}=0\times 39+x$$

8 daraja ko‘rsatkichini 10 ga hisoblang va 100000000 ni qiymatni oling.

$$24\times 100000000x^{2}=0\times 39+x$$

2400000000 hosil qilish uchun 24 va 100000000 ni ko'paytirish.

$$2400000000x^{2}=0\times 39+x$$

0 hosil qilish uchun 0 va 39 ni ko'paytirish.

$$2400000000x^{2}=0+x$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2400000000x^{2}=x$$

Ikkala tarafdan x ni ayirish.

$$2400000000x^{2}-x=0$$

Ikki tarafini 2400000000 ga bo‘ling.

$$\frac{2400000000x^{2}-x}{2400000000}=\frac{0}{2400000000}$$

2400000000 ga bo'lish 2400000000 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{1}{2400000000}x=\frac{0}{2400000000}$$

0 ni 2400000000 ga bo'lish.

$$x^{2}-\frac{1}{2400000000}x=0$$

-\frac{1}{2400000000} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{4800000000} olish uchun. Keyin, -\frac{1}{4800000000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{2400000000}x+\left(-\frac{1}{4800000000}\right)^{2}=\left(-\frac{1}{4800000000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{4800000000} kvadratini chiqarish.

$$x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000}=\frac{1}{23040000000000000000}$$

x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{4800000000}\right)^{2}=\frac{1}{23040000000000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{4800000000}\right)^{2}}=\sqrt{\frac{1}{23040000000000000000}}$$

Qisqartirish.

$$x-\frac{1}{4800000000}=\frac{1}{4800000000} x-\frac{1}{4800000000}=-\frac{1}{4800000000}$$

\frac{1}{4800000000} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{2400000000} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=\frac{1}{2400000000}$$