120000=112*812{left(x/1000right)}^2 eching

$$120000 = 112 \cdot 812 { \left( \frac{ x }{ 1000 } \right) }^{ 2 }$$

x uchun yechish

$$x = \frac{25000 \sqrt{87}}{203} \approx 1148,692001612$$

$$x = -\frac{25000 \sqrt{87}}{203} \approx -1148,692001612$$

Kvadrat ildizini topish bo'yicha qadamlar

90944 hosil qilish uchun 112 va 812 ni ko'paytirish.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

\frac{x}{1000}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

90944\times \frac{x^{2}}{1000^{2}} ni yagona kasrga aylantiring.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

2 daraja ko‘rsatkichini 1000 ga hisoblang va 1000000 ni qiymatni oling.

$$120000=\frac{90944x^{2}}{1000000}$$

\frac{1421}{15625}x^{2} ni olish uchun 90944x^{2} ni 1000000 ga bo‘ling.

$$120000=\frac{1421}{15625}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1421}{15625}x^{2}=120000$$

Ikki tarafini \frac{15625}{1421} va teskari kasri \frac{1421}{15625} ga ko‘paytiring.

$$x^{2}=120000\times \frac{15625}{1421}$$

\frac{1875000000}{1421} hosil qilish uchun 120000 va \frac{15625}{1421} ni ko'paytirish.

$$x^{2}=\frac{1875000000}{1421}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$

Kvadrat tenglamalaridan foydalanish qoidalari

90944 hosil qilish uchun 112 va 812 ni ko'paytirish.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

\frac{x}{1000}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

90944\times \frac{x^{2}}{1000^{2}} ni yagona kasrga aylantiring.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

2 daraja ko‘rsatkichini 1000 ga hisoblang va 1000000 ni qiymatni oling.

$$120000=\frac{90944x^{2}}{1000000}$$

\frac{1421}{15625}x^{2} ni olish uchun 90944x^{2} ni 1000000 ga bo‘ling.

$$120000=\frac{1421}{15625}x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{1421}{15625}x^{2}=120000$$

Ikkala tarafdan 120000 ni ayirish.

$$\frac{1421}{15625}x^{2}-120000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1421}{15625} ni a, 0 ni b va -120000 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

-4 ni \frac{1421}{15625} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{5684}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

-\frac{5684}{15625} ni -120000 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{1091328}{25}}}{2\times \frac{1421}{15625}}$$

\frac{1091328}{25} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{2\times \frac{1421}{15625}}$$

2 ni \frac{1421}{15625} marotabaga ko'paytirish.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}}$$

x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} tenglamasini yeching, bunda ± musbat.

$$x=\frac{25000\sqrt{87}}{203}$$

x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{25000\sqrt{87}}{203}$$

Tenglama yechildi.

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$