43897+204x^2=-59414x^2+13216x+52929 eching

$$43897+204 { x }^{ 2 } =-59414 { x }^{ 2 } +13216x+52929$$

x uchun yechish

$$x=\frac{2\sqrt{36383465}+3304}{29809}\approx 0,515540325$$

$$x=\frac{3304-2\sqrt{36383465}}{29809}\approx -0,293862308$$

Kvadrat tenglamalaridan foydalanish qoidalari

59414x^{2} ni ikki tarafga qo’shing.

$$43897+204x^{2}+59414x^{2}=13216x+52929$$

59618x^{2} ni olish uchun 204x^{2} va 59414x^{2} ni birlashtirish.

$$43897+59618x^{2}=13216x+52929$$

Ikkala tarafdan 13216x ni ayirish.

$$43897+59618x^{2}-13216x=52929$$

Ikkala tarafdan 52929 ni ayirish.

$$43897+59618x^{2}-13216x-52929=0$$

-9032 olish uchun 43897 dan 52929 ni ayirish.

$$-9032+59618x^{2}-13216x=0$$

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.

$$59618x^{2}-13216x-9032=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 59618 ni a, -13216 ni b va -9032 ni c bilan almashtiring.

$$x=\frac{-\left(-13216\right)±\sqrt{\left(-13216\right)^{2}-4\times 59618\left(-9032\right)}}{2\times 59618}$$

-13216 kvadratini chiqarish.

$$x=\frac{-\left(-13216\right)±\sqrt{174662656-4\times 59618\left(-9032\right)}}{2\times 59618}$$

-4 ni 59618 marotabaga ko'paytirish.

$$x=\frac{-\left(-13216\right)±\sqrt{174662656-238472\left(-9032\right)}}{2\times 59618}$$

-238472 ni -9032 marotabaga ko'paytirish.

$$x=\frac{-\left(-13216\right)±\sqrt{174662656+2153879104}}{2\times 59618}$$

174662656 ni 2153879104 ga qo'shish.

$$x=\frac{-\left(-13216\right)±\sqrt{2328541760}}{2\times 59618}$$

2328541760 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-13216\right)±8\sqrt{36383465}}{2\times 59618}$$

-13216 ning teskarisi 13216 ga teng.

$$x=\frac{13216±8\sqrt{36383465}}{2\times 59618}$$

2 ni 59618 marotabaga ko'paytirish.

$$x=\frac{13216±8\sqrt{36383465}}{119236}$$

x=\frac{13216±8\sqrt{36383465}}{119236} tenglamasini yeching, bunda ± musbat. 13216 ni 8\sqrt{36383465} ga qo'shish.

$$x=\frac{8\sqrt{36383465}+13216}{119236}$$

13216+8\sqrt{36383465} ni 119236 ga bo'lish.

$$x=\frac{2\sqrt{36383465}+3304}{29809}$$

x=\frac{13216±8\sqrt{36383465}}{119236} tenglamasini yeching, bunda ± manfiy. 13216 dan 8\sqrt{36383465} ni ayirish.

$$x=\frac{13216-8\sqrt{36383465}}{119236}$$

13216-8\sqrt{36383465} ni 119236 ga bo'lish.

$$x=\frac{3304-2\sqrt{36383465}}{29809}$$

Tenglama yechildi.

$$x=\frac{2\sqrt{36383465}+3304}{29809} x=\frac{3304-2\sqrt{36383465}}{29809}$$

Kvadratni yakunlash bo'yicha qadamlar

59414x^{2} ni ikki tarafga qo’shing.

$$43897+204x^{2}+59414x^{2}=13216x+52929$$

59618x^{2} ni olish uchun 204x^{2} va 59414x^{2} ni birlashtirish.

$$43897+59618x^{2}=13216x+52929$$

Ikkala tarafdan 13216x ni ayirish.

$$43897+59618x^{2}-13216x=52929$$

Ikkala tarafdan 43897 ni ayirish.

$$59618x^{2}-13216x=52929-43897$$

9032 olish uchun 52929 dan 43897 ni ayirish.

$$59618x^{2}-13216x=9032$$

Ikki tarafini 59618 ga bo‘ling.

$$\frac{59618x^{2}-13216x}{59618}=\frac{9032}{59618}$$

59618 ga bo'lish 59618 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{13216}{59618}\right)x=\frac{9032}{59618}$$

\frac{-13216}{59618} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{6608}{29809}x=\frac{9032}{59618}$$

\frac{9032}{59618} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{6608}{29809}x=\frac{4516}{29809}$$

-\frac{6608}{29809} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3304}{29809} olish uchun. Keyin, -\frac{3304}{29809} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{6608}{29809}x+\left(-\frac{3304}{29809}\right)^{2}=\frac{4516}{29809}+\left(-\frac{3304}{29809}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3304}{29809} kvadratini chiqarish.

$$x^{2}-\frac{6608}{29809}x+\frac{10916416}{888576481}=\frac{4516}{29809}+\frac{10916416}{888576481}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4516}{29809} ni \frac{10916416}{888576481} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{6608}{29809}x+\frac{10916416}{888576481}=\frac{145533860}{888576481}$$

x^{2}-\frac{6608}{29809}x+\frac{10916416}{888576481} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3304}{29809}\right)^{2}=\frac{145533860}{888576481}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3304}{29809}\right)^{2}}=\sqrt{\frac{145533860}{888576481}}$$

Qisqartirish.

$$x-\frac{3304}{29809}=\frac{2\sqrt{36383465}}{29809} x-\frac{3304}{29809}=-\frac{2\sqrt{36383465}}{29809}$$

\frac{3304}{29809} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{2\sqrt{36383465}+3304}{29809} x=\frac{3304-2\sqrt{36383465}}{29809}$$