185*10^6=143*400left(950-x^2/2right) eching

$$185 \times { 10 }^{ 6 } = 143 \cdot 400 \left( 950- \frac{ { x }^{ 2 } }{ 2 } \right)$$

x uchun yechish (complex solution)

$$x=-\frac{10\sqrt{934219}i}{143}\approx -0-67,590912618i$$

$$x=\frac{10\sqrt{934219}i}{143}\approx 67,590912618i$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

6 daraja ko‘rsatkichini 10 ga hisoblang va 1000000 ni qiymatni oling.

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

370000000 hosil qilish uchun 370 va 1000000 ni ko'paytirish.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

114400 hosil qilish uchun 286 va 400 ni ko'paytirish.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

114400 ga 950-\frac{x^{2}}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

114400 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$370000000=108680000-57200x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$108680000-57200x^{2}=370000000$$

Ikkala tarafdan 108680000 ni ayirish.

$$-57200x^{2}=370000000-108680000$$

261320000 olish uchun 370000000 dan 108680000 ni ayirish.

$$-57200x^{2}=261320000$$

Ikki tarafini -57200 ga bo‘ling.

$$x^{2}=\frac{261320000}{-57200}$$

\frac{261320000}{-57200} ulushini 400 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=-\frac{653300}{143}$$

Tenglama yechildi.

$$x=\frac{10\sqrt{934219}i}{143} x=-\frac{10\sqrt{934219}i}{143}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

6 daraja ko‘rsatkichini 10 ga hisoblang va 1000000 ni qiymatni oling.

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

370000000 hosil qilish uchun 370 va 1000000 ni ko'paytirish.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

114400 hosil qilish uchun 286 va 400 ni ko'paytirish.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

114400 ga 950-\frac{x^{2}}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

114400 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$370000000=108680000-57200x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$108680000-57200x^{2}=370000000$$

Ikkala tarafdan 370000000 ni ayirish.

$$108680000-57200x^{2}-370000000=0$$

-261320000 olish uchun 108680000 dan 370000000 ni ayirish.

$$-261320000-57200x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-57200x^{2}-261320000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -57200 ni a, 0 ni b va -261320000 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

-4 ni -57200 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{228800\left(-261320000\right)}}{2\left(-57200\right)}$$

228800 ni -261320000 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-59790016000000}}{2\left(-57200\right)}$$

-59790016000000 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8000\sqrt{934219}i}{2\left(-57200\right)}$$

2 ni -57200 marotabaga ko'paytirish.

$$x=\frac{0±8000\sqrt{934219}i}{-114400}$$

x=\frac{0±8000\sqrt{934219}i}{-114400} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{10\sqrt{934219}i}{143}$$

x=\frac{0±8000\sqrt{934219}i}{-114400} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{10\sqrt{934219}i}{143}$$

Tenglama yechildi.

$$x=-\frac{10\sqrt{934219}i}{143} x=\frac{10\sqrt{934219}i}{143}$$