x^2+985565x+2=0 eching

$${ x }^{ 2 } +985565x+2=0$$

x uchun yechish

$$x=\frac{\sqrt{971338369217}-985565}{2}\approx -0,000002029$$

$$x=\frac{-\sqrt{971338369217}-985565}{2}\approx -985564,999997971$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}+985565x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 985565 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-985565±\sqrt{985565^{2}-4\times 2}}{2}$$

985565 kvadratini chiqarish.

$$x=\frac{-985565±\sqrt{971338369225-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-985565±\sqrt{971338369225-8}}{2}$$

971338369225 ni -8 ga qo'shish.

$$x=\frac{-985565±\sqrt{971338369217}}{2}$$

x=\frac{-985565±\sqrt{971338369217}}{2} tenglamasini yeching, bunda ± musbat. -985565 ni \sqrt{971338369217} ga qo'shish.

$$x=\frac{\sqrt{971338369217}-985565}{2}$$

x=\frac{-985565±\sqrt{971338369217}}{2} tenglamasini yeching, bunda ± manfiy. -985565 dan \sqrt{971338369217} ni ayirish.

$$x=\frac{-\sqrt{971338369217}-985565}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{971338369217}-985565}{2} x=\frac{-\sqrt{971338369217}-985565}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+985565x+2=0$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x^{2}+985565x+2-2=-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x^{2}+985565x=-2$$

985565 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{985565}{2} olish uchun. Keyin, \frac{985565}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+985565x+\left(\frac{985565}{2}\right)^{2}=-2+\left(\frac{985565}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{985565}{2} kvadratini chiqarish.

$$x^{2}+985565x+\frac{971338369225}{4}=-2+\frac{971338369225}{4}$$

-2 ni \frac{971338369225}{4} ga qo'shish.

$$x^{2}+985565x+\frac{971338369225}{4}=\frac{971338369217}{4}$$

x^{2}+985565x+\frac{971338369225}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{985565}{2}\right)^{2}=\frac{971338369217}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{985565}{2}\right)^{2}}=\sqrt{\frac{971338369217}{4}}$$

Qisqartirish.

$$x+\frac{985565}{2}=\frac{\sqrt{971338369217}}{2} x+\frac{985565}{2}=-\frac{\sqrt{971338369217}}{2}$$

Tenglamaning ikkala tarafidan \frac{985565}{2} ni ayirish.

$$x=\frac{\sqrt{971338369217}-985565}{2} x=\frac{-\sqrt{971338369217}-985565}{2}$$