x=425x^2+635x-39075 eching

$$x=425 { x }^{ 2 } +635x-39075$$

x uchun yechish

$$x = \frac{2 \sqrt{4176841} - 317}{425} \approx 8,87168059$$

$$x=\frac{-2\sqrt{4176841}-317}{425}\approx -10,363445296$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 425x^{2} ni ayirish.

$$x-425x^{2}=635x-39075$$

Ikkala tarafdan 635x ni ayirish.

$$x-425x^{2}-635x=-39075$$

-634x ni olish uchun x va -635x ni birlashtirish.

$$-634x-425x^{2}=-39075$$

39075 ni ikki tarafga qo’shing.

$$-634x-425x^{2}+39075=0$$

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.

$$-425x^{2}-634x+39075=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -425 ni a, -634 ni b va 39075 ni c bilan almashtiring.

$$x=\frac{-\left(-634\right)±\sqrt{\left(-634\right)^{2}-4\left(-425\right)\times 39075}}{2\left(-425\right)}$$

-634 kvadratini chiqarish.

$$x=\frac{-\left(-634\right)±\sqrt{401956-4\left(-425\right)\times 39075}}{2\left(-425\right)}$$

-4 ni -425 marotabaga ko'paytirish.

$$x=\frac{-\left(-634\right)±\sqrt{401956+1700\times 39075}}{2\left(-425\right)}$$

1700 ni 39075 marotabaga ko'paytirish.

$$x=\frac{-\left(-634\right)±\sqrt{401956+66427500}}{2\left(-425\right)}$$

401956 ni 66427500 ga qo'shish.

$$x=\frac{-\left(-634\right)±\sqrt{66829456}}{2\left(-425\right)}$$

66829456 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-634\right)±4\sqrt{4176841}}{2\left(-425\right)}$$

-634 ning teskarisi 634 ga teng.

$$x=\frac{634±4\sqrt{4176841}}{2\left(-425\right)}$$

2 ni -425 marotabaga ko'paytirish.

$$x=\frac{634±4\sqrt{4176841}}{-850}$$

x=\frac{634±4\sqrt{4176841}}{-850} tenglamasini yeching, bunda ± musbat. 634 ni 4\sqrt{4176841} ga qo'shish.

$$x=\frac{4\sqrt{4176841}+634}{-850}$$

634+4\sqrt{4176841} ni -850 ga bo'lish.

$$x=\frac{-2\sqrt{4176841}-317}{425}$$

x=\frac{634±4\sqrt{4176841}}{-850} tenglamasini yeching, bunda ± manfiy. 634 dan 4\sqrt{4176841} ni ayirish.

$$x=\frac{634-4\sqrt{4176841}}{-850}$$

634-4\sqrt{4176841} ni -850 ga bo'lish.

$$x=\frac{2\sqrt{4176841}-317}{425}$$

Tenglama yechildi.

$$x=\frac{-2\sqrt{4176841}-317}{425} x=\frac{2\sqrt{4176841}-317}{425}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 425x^{2} ni ayirish.

$$x-425x^{2}=635x-39075$$

Ikkala tarafdan 635x ni ayirish.

$$x-425x^{2}-635x=-39075$$

-634x ni olish uchun x va -635x ni birlashtirish.

$$-634x-425x^{2}=-39075$$

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

$$-425x^{2}-634x=-39075$$

Ikki tarafini -425 ga bo‘ling.

$$\frac{-425x^{2}-634x}{-425}=-\frac{39075}{-425}$$

-425 ga bo'lish -425 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{634}{-425}\right)x=-\frac{39075}{-425}$$

-634 ni -425 ga bo'lish.

$$x^{2}+\frac{634}{425}x=-\frac{39075}{-425}$$

\frac{-39075}{-425} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{634}{425}x=\frac{1563}{17}$$

\frac{634}{425} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{317}{425} olish uchun. Keyin, \frac{317}{425} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{634}{425}x+\left(\frac{317}{425}\right)^{2}=\frac{1563}{17}+\left(\frac{317}{425}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{317}{425} kvadratini chiqarish.

$$x^{2}+\frac{634}{425}x+\frac{100489}{180625}=\frac{1563}{17}+\frac{100489}{180625}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1563}{17} ni \frac{100489}{180625} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{634}{425}x+\frac{100489}{180625}=\frac{16707364}{180625}$$

x^{2}+\frac{634}{425}x+\frac{100489}{180625} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{317}{425}\right)^{2}=\frac{16707364}{180625}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{317}{425}\right)^{2}}=\sqrt{\frac{16707364}{180625}}$$

Qisqartirish.

$$x+\frac{317}{425}=\frac{2\sqrt{4176841}}{425} x+\frac{317}{425}=-\frac{2\sqrt{4176841}}{425}$$

Tenglamaning ikkala tarafidan \frac{317}{425} ni ayirish.

$$x=\frac{2\sqrt{4176841}-317}{425} x=\frac{-2\sqrt{4176841}-317}{425}$$